def describe_scalars(self, v, plane):
axes = plane.get_axes()
long_v = Vector(2*v.get_end())
long_minus_v = Vector(-2*v.get_end())
original_v = v.copy()
scaling_word = TextMobject("``Scaling''").to_corner(UP+LEFT)
scaling_word.shift(2*RIGHT)
scalars = VMobject(*map(TexMobject, [
"2,", "\\dfrac{1}{3},", "-1.8,", "\\dots"
]))
scalars.arrange_submobjects(RIGHT, buff = 0.4)
scalars.next_to(scaling_word, DOWN, aligned_edge = LEFT)
scalars_word = TextMobject("``Scalars''")
scalars_word.next_to(scalars, DOWN, aligned_edge = LEFT)
self.remove(plane)
self.add(axes)
self.play(
Write(scaling_word),
Transform(v, long_v),
run_time = 1.5
)
self.play(Transform(v, long_minus_v, run_time = 3))
self.play(Write(scalars))
self.wait()
self.play(Write(scalars_word))
self.play(Transform(v, original_v), run_time = 3)
self.wait(2)
def construct(self):
matrix = Matrix([
[2, 0],
[-1, 1],
[-2, 1],
])
matrix.highlight_columns(X_COLOR, Y_COLOR)
brace = Brace(matrix)
words = VMobject(
TextMobject("Span", "of columns"),
TexMobject("\\Updownarrow"),
TextMobject("``Column space''")
)
words.arrange_submobjects(DOWN, buff = 0.1)
words.next_to(brace, DOWN)
words[0][0].highlight(PINK)
words[2].highlight(TEAL)
words[0].add_background_rectangle()
words[2].add_background_rectangle()
VMobject(matrix, brace, words).center()
self.add(matrix)
self.play(
GrowFromCenter(brace),
Write(words, run_time = 2)
)
self.wait()
def add_scaling(self, arrows, syms, arrays):
s_arrows = VMobject(
TexMobject("2"), Vector([1, 1]).highlight(YELLOW),
TexMobject("="), Vector([2, 2]).highlight(WHITE)
)
s_arrows.arrange_submobjects(RIGHT)
s_arrows.scale(0.75)
s_arrows.next_to(arrows, DOWN)
s_arrays = VMobject(
TexMobject("2"),
matrix_to_mobject([3, -5]).highlight(YELLOW),
TextMobject("="),
matrix_to_mobject(["2(3)", "2(-5)"])
)
s_arrays.arrange_submobjects(RIGHT)
s_arrays.scale(0.75)
s_arrays.next_to(arrays, DOWN)
s_syms = TexMobject(["2", "\\vec{\\textbf{v}}"])
s_syms.split()[-1].highlight(YELLOW)
s_syms.next_to(syms, DOWN)
self.play(
Write(s_arrows), Write(s_arrays), Write(s_syms),
run_time = 2
)
self.wait()
def add_scaling(self, arrows, syms, arrays):
s_arrows = VMobject(
TexMobject("2"), Vector([1, 1]).highlight(YELLOW),
TexMobject("="), Vector([2, 2]).highlight(WHITE)
)
s_arrows.arrange_submobjects(RIGHT)
s_arrows.scale(0.75)
s_arrows.next_to(arrows, DOWN)
s_arrays = VMobject(
TexMobject("2"),
matrix_to_mobject([3, -5]).highlight(YELLOW),
TextMobject("="),
matrix_to_mobject(["2(3)", "2(-5)"])
)
s_arrays.arrange_submobjects(RIGHT)
s_arrays.scale(0.5)
s_arrays.next_to(arrays, DOWN)
s_syms = TexMobject(["2", "\\vec{\\textbf{v}}"])
s_syms.split()[-1].highlight(YELLOW)
s_syms.next_to(syms, DOWN)
self.play(
Write(s_arrows), Write(s_arrays), Write(s_syms),
run_time = 2
)
self.dither()
def show_dependencies(self):
linalg = TextMobject("Linear Algebra")
subjects = map(TextMobject, [
"Computer science",
"Physics",
"Electrical engineering",
"Mechanical engineering",
"Statistics",
"\\vdots"
])
prev = subjects[0]
for subject in subjects[1:]:
subject.next_to(prev, DOWN, aligned_edge = LEFT)
prev = subject
all_subs = VMobject(*subjects)
linalg.to_edge(LEFT)
all_subs.next_to(linalg, RIGHT, buff = 2)
arrows = VMobject(*[
Arrow(linalg, sub)
for sub in subjects
])
self.play(Write(linalg, run_time = 1))
self.dither()
self.play(
ShowCreation(arrows, submobject_mode = "lagged_start"),
FadeIn(all_subs),
run_time = 2
)
self.dither()
self.linalg = linalg
def describe_scalars(self, v, plane):
axes = plane.get_axes()
long_v = Vector(2*v.get_end())
long_minus_v = Vector(-2*v.get_end())
original_v = v.copy()
scaling_word = TextMobject("``Scaling''").to_corner(UP+LEFT)
scaling_word.shift(2*RIGHT)
scalars = VMobject(*map(TexMobject, [
"2,", "\\dfrac{1}{3},", "-1.8,", "\\dots"
]))
scalars.arrange_submobjects(RIGHT, buff = 0.4)
scalars.next_to(scaling_word, DOWN, aligned_edge = LEFT)
scalars_word = TextMobject("``Scalars''")
scalars_word.next_to(scalars, DOWN, aligned_edge = LEFT)
self.remove(plane)
self.add(axes)
self.play(
Write(scaling_word),
Transform(v, long_v),
run_time = 1.5
)
self.play(Transform(v, long_minus_v, run_time = 3))
self.play(Write(scalars))
self.dither()
self.play(Write(scalars_word))
self.play(Transform(v, original_v), run_time = 3)
self.dither(2)
def construct(self):
matrix = Matrix([
[2, 0],
[-1, 1],
[-2, 1],
])
matrix.highlight_columns(X_COLOR, Y_COLOR)
brace = Brace(matrix)
words = VMobject(
TextMobject("Span", "of columns"),
TexMobject("\\Updownarrow"),
TextMobject("``Column space''")
)
words.arrange_submobjects(DOWN, buff = 0.1)
words.next_to(brace, DOWN)
words[0][0].highlight(PINK)
words[2].highlight(TEAL)
words[0].add_background_rectangle()
words[2].add_background_rectangle()
VMobject(matrix, brace, words).center()
self.add(matrix)
self.play(
GrowFromCenter(brace),
Write(words, run_time = 2)
)
self.dither()
def construct(self):
title = TextMobject("Essence of Linear Algebra")
title.highlight(BLUE)
title.to_corner(UP+LEFT)
h_line = Line(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
h_line.next_to(title, DOWN)
h_line.to_edge(LEFT, buff = 0)
chapters = VMobject(*map(TextMobject, [
"Chapter 1: Vectors, what even are they?",
"Chapter 2: Linear combinations, span and bases",
"Chapter 3: Matrices as linear transformations",
"Chapter 4: Matrix multiplication as composition",
"Chapter 5: The determinant",
"Chapter 6: Inverse matrices, column space and null space",
"Chapter 7: Dot products and cross products",
"Chapter 8: Change of basis",
"Chapter 9: Eigenvectors and eigenvalues",
"Chapter 10: Abstract vector spaces",
]))
chapters.arrange_submobjects(DOWN)
chapters.scale(0.7)
chapters.next_to(h_line, DOWN)
self.play(
Write(title),
ShowCreation(h_line)
)
for chapter in chapters.split():
chapter.to_edge(LEFT, buff = 1)
self.play(FadeIn(chapter))
self.dither(2)
entry3 = chapters.split()[2]
added_words = TextMobject("(Personally, I'm most excited \\\\ to do this one)")
added_words.scale(0.5)
added_words.highlight(YELLOW)
added_words.next_to(h_line, DOWN)
added_words.to_edge(RIGHT)
arrow = Arrow(added_words.get_bottom(), entry3)
self.play(
ApplyMethod(entry3.highlight, YELLOW),
ShowCreation(arrow, submobject_mode = "one_at_a_time"),
Write(added_words),
run_time = 1
)
self.dither()
removeable = VMobject(added_words, arrow, h_line, title)
self.play(FadeOut(removeable))
self.remove(removeable)
self.series_of_videos(chapters)
def show_formula(self):
matrix = self.get_matrix()
det_text = get_det_text(matrix)
f_str = "=(a+b)(c+d)-ac-bd-2bc=ad-bc"
formula = TexMobject(f_str)
formula.next_to(det_text, RIGHT)
everyone = VMobject(det_text, matrix, formula)
everyone.scale_to_fit_width(2 * SPACE_WIDTH - 1)
everyone.next_to(DOWN, DOWN)
background_rect = BackgroundRectangle(everyone)
self.play(ShowCreation(background_rect), Write(everyone))
self.wait()
def construct(self):
title = TextMobject("Essence of Linear Algebra")
title.highlight(BLUE)
title.to_corner(UP + LEFT)
h_line = Line(SPACE_WIDTH * LEFT, SPACE_WIDTH * RIGHT)
h_line.next_to(title, DOWN)
h_line.to_edge(LEFT, buff=0)
chapters = VMobject(*map(TextMobject, [
"Chapter 1: Vectors, what even are they?",
"Chapter 2: Linear combinations, span and bases",
"Chapter 3: Matrices as linear transformations",
"Chapter 4: Matrix multiplication as composition",
"Chapter 5: The determinant",
"Chapter 6: Inverse matrices, column space and null space",
"Chapter 7: Dot products and cross products",
"Chapter 8: Change of basis",
"Chapter 9: Eigenvectors and eigenvalues",
"Chapter 10: Abstract vector spaces",
]))
chapters.arrange_submobjects(DOWN)
chapters.scale(0.7)
chapters.next_to(h_line, DOWN)
self.play(Write(title), ShowCreation(h_line))
for chapter in chapters.split():
chapter.to_edge(LEFT, buff=1)
self.play(FadeIn(chapter))
self.wait(2)
entry3 = chapters.split()[2]
added_words = TextMobject(
"(Personally, I'm most excited \\\\ to do this one)")
added_words.scale(0.5)
added_words.highlight(YELLOW)
added_words.next_to(h_line, DOWN)
added_words.to_edge(RIGHT)
arrow = Arrow(added_words.get_bottom(), entry3)
self.play(ApplyMethod(entry3.highlight, YELLOW),
ShowCreation(arrow, submobject_mode="one_at_a_time"),
Write(added_words),
run_time=1)
self.wait()
removeable = VMobject(added_words, arrow, h_line, title)
self.play(FadeOut(removeable))
self.remove(removeable)
self.series_of_videos(chapters)
def show_formula(self):
matrix = self.get_matrix()
det_text = get_det_text(matrix)
f_str = "=(a+b)(c+d)-ac-bd-2bc=ad-bc"
formula = TexMobject(f_str)
formula.next_to(det_text, RIGHT)
everyone = VMobject(det_text, matrix, formula)
everyone.scale_to_fit_width(2*SPACE_WIDTH - 1)
everyone.next_to(DOWN, DOWN)
background_rect = BackgroundRectangle(everyone)
self.play(
ShowCreation(background_rect),
Write(everyone)
)
self.dither()
def construct(self):
self.setup()
matrix = Matrix(np.array(self.transposed_matrix).transpose())
matrix.highlight_columns(X_COLOR, Y_COLOR)
matrix.next_to(ORIGIN, LEFT).to_edge(UP)
matrix_background = BackgroundRectangle(matrix)
self.play(ShowCreation(matrix_background), Write(matrix))
if self.show_square:
self.add_unit_square(animate = True)
self.add_foreground_mobject(matrix_background, matrix)
self.dither()
self.apply_transposed_matrix([self.transposed_matrix[0], [0, 1]])
self.apply_transposed_matrix([[1, 0], self.transposed_matrix[1]])
self.dither()
if self.show_square:
bottom_brace = Brace(self.i_hat, DOWN)
right_brace = Brace(self.square, RIGHT)
width = TexMobject(str(self.transposed_matrix[0][0]))
height = TexMobject(str(self.transposed_matrix[1][1]))
width.next_to(bottom_brace, DOWN)
height.next_to(right_brace, RIGHT)
for mob in bottom_brace, width, right_brace, height:
mob.add_background_rectangle()
self.play(Write(mob, run_time = 0.5))
self.dither()
width_target, height_target = width.copy(), height.copy()
det = np.linalg.det(self.transposed_matrix)
times, eq_det = map(TexMobject, ["\\times", "=%d"%det])
words = TextMobject("New area $=$")
equation = VMobject(
words, width_target, times, height_target, eq_det
)
equation.arrange_submobjects(RIGHT, buff = 0.2)
equation.next_to(self.square, UP, aligned_edge = LEFT)
equation.shift(0.5*RIGHT)
background_rect = BackgroundRectangle(equation)
self.play(
ShowCreation(background_rect),
Transform(width.copy(), width_target),
Transform(height.copy(), height_target),
*map(Write, [words, times, eq_det])
)
self.dither()
def construct(self):
morty = Mortimer()
morty.scale(0.8)
morty.to_corner(DOWN+RIGHT)
morty.shift(0.5*LEFT)
title = TextMobject("Associativity:")
title.to_corner(UP+LEFT)
lhs = TexMobject(list("(AB)C"))
lp, a, b, rp, c = lhs.split()
rhs = VMobject(*[m.copy() for m in a, lp, b, c, rp])
point = VectorizedPoint()
start = VMobject(*[m.copy() for m in point, a, b, point, c])
for mob in lhs, rhs, start:
mob.arrange_submobjects(buff = 0.1)
a, lp, b, c, rp = rhs.split()
rhs = VMobject(lp, a, b, rp, c)##Align order to lhs
eq = TexMobject("=")
q_marks = TextMobject("???")
q_marks.submobject_gradient_highlight(TEAL_B, TEAL_D)
q_marks.next_to(eq, UP)
lhs.next_to(eq, LEFT)
rhs.next_to(eq, RIGHT)
start.move_to(lhs)
self.add(morty, title)
self.dither()
self.play(Blink(morty))
self.play(Write(start))
self.dither()
self.play(Transform(start, lhs))
self.dither()
self.play(
Transform(lhs, rhs, path_arc = -np.pi),
Write(eq)
)
self.play(Write(q_marks))
self.play(Blink(morty))
self.play(morty.change_mode, "pondering")
lp, a, b, rp, c = start.split()
self.show_full_matrices(morty, a, b, c, title)
def construct(self):
self.setup()
matrix = Matrix(np.array(self.transposed_matrix).transpose())
matrix.highlight_columns(X_COLOR, Y_COLOR)
matrix.next_to(ORIGIN, LEFT).to_edge(UP)
matrix_background = BackgroundRectangle(matrix)
self.play(ShowCreation(matrix_background), Write(matrix))
if self.show_square:
self.add_unit_square(animate=True)
self.add_foreground_mobject(matrix_background, matrix)
self.wait()
self.apply_transposed_matrix([self.transposed_matrix[0], [0, 1]])
self.apply_transposed_matrix([[1, 0], self.transposed_matrix[1]])
self.wait()
if self.show_square:
bottom_brace = Brace(self.i_hat, DOWN)
right_brace = Brace(self.square, RIGHT)
width = TexMobject(str(self.transposed_matrix[0][0]))
height = TexMobject(str(self.transposed_matrix[1][1]))
width.next_to(bottom_brace, DOWN)
height.next_to(right_brace, RIGHT)
for mob in bottom_brace, width, right_brace, height:
mob.add_background_rectangle()
self.play(Write(mob, run_time=0.5))
self.wait()
width_target, height_target = width.copy(), height.copy()
det = np.linalg.det(self.transposed_matrix)
times, eq_det = map(TexMobject, ["\\times", "=%d" % det])
words = TextMobject("New area $=$")
equation = VMobject(words, width_target, times, height_target,
eq_det)
equation.arrange_submobjects(RIGHT, buff=0.2)
equation.next_to(self.square, UP, aligned_edge=LEFT)
equation.shift(0.5 * RIGHT)
background_rect = BackgroundRectangle(equation)
self.play(ShowCreation(background_rect),
Transform(width.copy(), width_target),
Transform(height.copy(), height_target),
*map(Write, [words, times, eq_det]))
self.wait()
def construct(self):
morty = Mortimer()
morty.scale(0.8)
morty.to_corner(DOWN + RIGHT)
morty.shift(0.5 * LEFT)
title = TextMobject("Associativity:")
title.to_corner(UP + LEFT)
lhs = TexMobject(list("(AB)C"))
lp, a, b, rp, c = lhs.split()
rhs = VMobject(*[m.copy() for m in a, lp, b, c, rp])
point = VectorizedPoint()
start = VMobject(*[m.copy() for m in point, a, b, point, c])
for mob in lhs, rhs, start:
mob.arrange_submobjects(buff=0.1)
a, lp, b, c, rp = rhs.split()
rhs = VMobject(lp, a, b, rp, c) ##Align order to lhs
eq = TexMobject("=")
q_marks = TextMobject("???")
q_marks.submobject_gradient_highlight(TEAL_B, TEAL_D)
q_marks.next_to(eq, UP)
lhs.next_to(eq, LEFT)
rhs.next_to(eq, RIGHT)
start.move_to(lhs)
self.add(morty, title)
self.wait()
self.play(Blink(morty))
self.play(Write(start))
self.wait()
self.play(Transform(start, lhs))
self.wait()
self.play(Transform(lhs, rhs, path_arc=-np.pi), Write(eq))
self.play(Write(q_marks))
self.play(Blink(morty))
self.play(morty.change_mode, "pondering")
lp, a, b, rp, c = start.split()
self.show_full_matrices(morty, a, b, c, title)
def show_dependencies(self):
linalg = TextMobject("Linear Algebra")
subjects = map(TextMobject, [
"Computer science", "Physics", "Electrical engineering",
"Mechanical engineering", "Statistics", "\\vdots"
])
prev = subjects[0]
for subject in subjects[1:]:
subject.next_to(prev, DOWN, aligned_edge=LEFT)
prev = subject
all_subs = VMobject(*subjects)
linalg.to_edge(LEFT)
all_subs.next_to(linalg, RIGHT, buff=2)
arrows = VMobject(*[Arrow(linalg, sub) for sub in subjects])
self.play(Write(linalg, run_time=1))
self.wait()
self.play(ShowCreation(arrows, submobject_mode="lagged_start"),
FadeIn(all_subs),
run_time=2)
self.wait()
self.linalg = linalg
def construct(self):
m1_mob, m2_mob, comp_matrix = self.get_matrices()
self.add(m1_mob, m2_mob, m1_mob.label, m2_mob.label, comp_matrix)
result = self.get_result()
col1, col2 = [
VMobject(*m1_mob.split()[1].get_mob_matrix()[:,i])
for i in 0, 1
]
col1.target_color = X_COLOR
col2.target_color = Y_COLOR
for col in col1, col2:
circle = Circle()
circle.stretch_to_fit_height(m1_mob.get_height())
circle.stretch_to_fit_width(m1_mob.get_width()/2.5)
circle.highlight(col.target_color)
circle.move_to(col)
col.circle = circle
triplets = [
(col1, "i", X_COLOR),
(col2, "j", Y_COLOR),
]
for i, (col, char, color) in enumerate(triplets):
self.add(col)
start_state = self.get_mobjects()
question = TextMobject(
"Where does $\\hat{\\%smath}$ go?"%char
)
question.split()[-4].highlight(color)
question.split()[-5].highlight(color)
question.scale(1.2)
question.shift(DOWN)
first = TextMobject("First here")
first.highlight(color)
first.shift(DOWN+LEFT)
first_arrow = Arrow(
first, col.circle.get_bottom(), color = color
)
second = TextMobject("Then to whatever this is")
second.highlight(color)
second.to_edge(RIGHT).shift(DOWN)
m2_copy = m2_mob.copy()
m2_target = m2_mob.copy()
m2_target.next_to(m2_mob, DOWN, buff = 1)
col_vect = Matrix(col.copy().split())
col_vect.highlight(color)
col_vect.next_to(m2_target, RIGHT, buff = 0.1)
second_arrow = Arrow(second, col_vect, color = color)
new_m2_copy = m2_mob.copy().split()[1]
intermediate = VMobject(
TexMobject("="),
col_vect.copy().get_entries().split()[0],
Matrix(new_m2_copy.get_mob_matrix()[:,0]),
TexMobject("+"),
col_vect.copy().get_entries().split()[1],
Matrix(new_m2_copy.get_mob_matrix()[:,1]),
TexMobject("=")
)
intermediate.arrange_submobjects(buff = 0.1)
intermediate.next_to(col_vect, RIGHT)
product = Matrix(result[:,i])
product.next_to(intermediate, RIGHT)
comp_col = VMobject(*comp_matrix.split()[1].get_mob_matrix()[:,i])
self.play(Write(question, run_time = 1 ))
self.dither()
self.play(
Transform(question, first),
ShowCreation(first_arrow),
ShowCreation(col.circle),
ApplyMethod(col.highlight, col.target_color)
)
self.dither()
self.play(
Transform(m2_copy, m2_target, run_time = 2),
ApplyMethod(col.copy().move_to, col_vect, run_time = 2),
Write(col_vect.get_brackets()),
Transform(first_arrow, second_arrow),
Transform(question, second),
)
self.dither()
self.play(*map(FadeOut, [question, first_arrow]))
self.play(Write(intermediate))
self.dither()
self.play(Write(product))
self.dither()
product_entries = product.get_entries()
self.play(
ApplyMethod(comp_col.highlight, BLACK),
ApplyMethod(product_entries.move_to, comp_col)
)
self.dither()
start_state.append(product_entries)
self.play(*[
FadeOut(mob)
for mob in self.get_mobjects()
if mob not in start_state
] + [
Animation(product_entries)
])
self.dither()
def construct(self):
vect = Matrix(["x", "y"])
vect.get_entries().highlight(YELLOW)
rot_matrix = Matrix([[0, -1], [1, 0]])
rot_matrix.highlight(TEAL)
shear_matrix = Matrix([[1, 1], [0, 1]])
shear_matrix.highlight(PINK)
l_paren, r_paren = map(TexMobject, ["\\Big(", "\\Big)"])
for p in l_paren, r_paren:
p.scale_to_fit_height(1.4 * vect.get_height())
long_way = VMobject(shear_matrix, l_paren, rot_matrix, vect, r_paren)
long_way.arrange_submobjects(buff=0.1)
long_way.to_edge(LEFT).shift(UP)
equals = TexMobject("=").next_to(long_way, RIGHT)
comp_matrix = Matrix([[1, -1], [1, 0]])
comp_matrix.highlight_columns(X_COLOR, Y_COLOR)
vect_copy = vect.copy()
short_way = VMobject(comp_matrix, vect_copy)
short_way.arrange_submobjects(buff=0.1)
short_way.next_to(equals, RIGHT)
pairs = [
(rot_matrix, "Rotation"),
(shear_matrix, "Shear"),
(comp_matrix, "Composition"),
]
for matrix, word in pairs:
brace = Brace(matrix)
text = TextMobject(word).next_to(brace, DOWN)
brace.highlight(matrix.get_color())
text.highlight(matrix.get_color())
matrix.add(brace, text)
comp_matrix.split()[-1].submobject_gradient_highlight(TEAL, PINK)
self.add(vect)
groups = [
[rot_matrix],
[l_paren, r_paren, shear_matrix],
[equals, comp_matrix, vect_copy],
]
for group in groups:
self.play(*map(Write, group))
self.wait()
self.play(*map(FadeOut, [l_paren, r_paren, vect, vect_copy]))
comp_matrix.add(equals)
matrices = VMobject(shear_matrix, rot_matrix, comp_matrix)
self.play(
ApplyMethod(matrices.arrange_submobjects,
buff=0.1,
aligned_edge=UP))
self.wait()
arrow = Arrow(rot_matrix.get_right(), shear_matrix.get_left())
arrow.shift((rot_matrix.get_top()[1] + 0.2) * UP)
words = TextMobject("Read right to left")
words.submobjects.reverse()
words.next_to(arrow, UP)
functions = TexMobject("f(g(x))")
functions.next_to(words, UP)
self.play(ShowCreation(arrow))
self.play(Write(words))
self.wait()
self.play(Write(functions))
self.wait()
def construct(self):
m1_mob, m2_mob, comp_matrix = self.get_matrices()
self.add(m1_mob, m2_mob, m1_mob.label, m2_mob.label, comp_matrix)
result = self.get_result()
col1, col2 = [
VMobject(*m1_mob.split()[1].get_mob_matrix()[:, i]) for i in 0, 1
]
col1.target_color = X_COLOR
col2.target_color = Y_COLOR
for col in col1, col2:
circle = Circle()
circle.stretch_to_fit_height(m1_mob.get_height())
circle.stretch_to_fit_width(m1_mob.get_width() / 2.5)
circle.highlight(col.target_color)
circle.move_to(col)
col.circle = circle
triplets = [
(col1, "i", X_COLOR),
(col2, "j", Y_COLOR),
]
for i, (col, char, color) in enumerate(triplets):
self.add(col)
start_state = self.get_mobjects()
question = TextMobject("Where does $\\hat{\\%smath}$ go?" % char)
question.split()[-4].highlight(color)
question.split()[-5].highlight(color)
question.scale(1.2)
question.shift(DOWN)
first = TextMobject("First here")
first.highlight(color)
first.shift(DOWN + LEFT)
first_arrow = Arrow(first, col.circle.get_bottom(), color=color)
second = TextMobject("Then to whatever this is")
second.highlight(color)
second.to_edge(RIGHT).shift(DOWN)
m2_copy = m2_mob.copy()
m2_target = m2_mob.copy()
m2_target.next_to(m2_mob, DOWN, buff=1)
col_vect = Matrix(col.copy().split())
col_vect.highlight(color)
col_vect.next_to(m2_target, RIGHT, buff=0.1)
second_arrow = Arrow(second, col_vect, color=color)
new_m2_copy = m2_mob.copy().split()[1]
intermediate = VMobject(TexMobject("="),
col_vect.copy().get_entries().split()[0],
Matrix(new_m2_copy.get_mob_matrix()[:, 0]),
TexMobject("+"),
col_vect.copy().get_entries().split()[1],
Matrix(new_m2_copy.get_mob_matrix()[:, 1]),
TexMobject("="))
intermediate.arrange_submobjects(buff=0.1)
intermediate.next_to(col_vect, RIGHT)
product = Matrix(result[:, i])
product.next_to(intermediate, RIGHT)
comp_col = VMobject(*comp_matrix.split()[1].get_mob_matrix()[:, i])
self.play(Write(question, run_time=1))
self.wait()
self.play(Transform(question, first), ShowCreation(first_arrow),
ShowCreation(col.circle),
ApplyMethod(col.highlight, col.target_color))
self.wait()
self.play(
Transform(m2_copy, m2_target, run_time=2),
ApplyMethod(col.copy().move_to, col_vect, run_time=2),
Write(col_vect.get_brackets()),
Transform(first_arrow, second_arrow),
Transform(question, second),
)
self.wait()
self.play(*map(FadeOut, [question, first_arrow]))
self.play(Write(intermediate))
self.wait()
self.play(Write(product))
self.wait()
product_entries = product.get_entries()
self.play(ApplyMethod(comp_col.highlight, BLACK),
ApplyMethod(product_entries.move_to, comp_col))
self.wait()
start_state.append(product_entries)
self.play(*[
FadeOut(mob)
for mob in self.get_mobjects() if mob not in start_state
] + [Animation(product_entries)])
self.wait()
def construct(self):
vect = Matrix(["x", "y"])
vect.get_entries().highlight(YELLOW)
rot_matrix = Matrix([[0, -1], [1, 0]])
rot_matrix.highlight(TEAL)
shear_matrix = Matrix([[1, 1], [0, 1]])
shear_matrix.highlight(PINK)
l_paren, r_paren = map(TexMobject, ["\\Big(", "\\Big)"])
for p in l_paren, r_paren:
p.scale_to_fit_height(1.4*vect.get_height())
long_way = VMobject(
shear_matrix, l_paren, rot_matrix, vect, r_paren
)
long_way.arrange_submobjects(buff = 0.1)
long_way.to_edge(LEFT).shift(UP)
equals = TexMobject("=").next_to(long_way, RIGHT)
comp_matrix = Matrix([[1, -1], [1, 0]])
comp_matrix.highlight_columns(X_COLOR, Y_COLOR)
vect_copy = vect.copy()
short_way = VMobject(comp_matrix, vect_copy)
short_way.arrange_submobjects(buff = 0.1)
short_way.next_to(equals, RIGHT)
pairs = [
(rot_matrix, "Rotation"),
(shear_matrix, "Shear"),
(comp_matrix, "Composition"),
]
for matrix, word in pairs:
brace = Brace(matrix)
text = TextMobject(word).next_to(brace, DOWN)
brace.highlight(matrix.get_color())
text.highlight(matrix.get_color())
matrix.add(brace, text)
comp_matrix.split()[-1].submobject_gradient_highlight(TEAL, PINK)
self.add(vect)
groups = [
[rot_matrix],
[l_paren, r_paren, shear_matrix],
[equals, comp_matrix, vect_copy],
]
for group in groups:
self.play(*map(Write, group))
self.dither()
self.play(*map(FadeOut, [l_paren, r_paren, vect, vect_copy]))
comp_matrix.add(equals)
matrices = VMobject(shear_matrix, rot_matrix, comp_matrix)
self.play(ApplyMethod(
matrices.arrange_submobjects, buff = 0.1,
aligned_edge = UP
))
self.dither()
arrow = Arrow(rot_matrix.get_right(), shear_matrix.get_left())
arrow.shift((rot_matrix.get_top()[1]+0.2)*UP)
words = TextMobject("Read right to left")
words.submobjects.reverse()
words.next_to(arrow, UP)
functions = TexMobject("f(g(x))")
functions.next_to(words, UP)
self.play(ShowCreation(arrow))
self.play(Write(words))
self.dither()
self.play(Write(functions))
self.dither()
