線性變換的概念
Author: 藍邦偉  老師

線性變換的概念

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\left [\begin{array}{cc} a & b \ c & d \ \end{array}   \right ] \left [ \begin{array}{cc} x \ y \ \end{array}  \right ] =\left [  \begin{array}{cc} ax+by \ cx+dy \ \end{array} \right ] 

滑竿輸入

a

b

c

d

輸入框輸入

a=

b=

c=

d=

x

y

d = 1 (slider from -5 to 5, step 1)
c = 0 (slider from -5 to 5, step 1)
b = 0 (slider from -5 to 5, step 1)
a = 1 (slider from -5 to 5, step 1)
L = 1.2 (slider from 0.1 to 2, step 0.1)
O = (0, 0)
A_1: (a * (-L) / 2 + b * (-L) / 2, c * (-L) / 2 + d * (-L) / 2)
A_2: (a * L / 2 + b * (-L) / 2, c * L / 2 + d * (-L) / 2)
A_3: (a * L / 2 + b * L / 2, c * L / 2 + d * L / 2)
A_4: (a * (-L) / 2 + b * L / 2, c * (-L) / 2 + d * L / 2)
b_1 = Segment(A_4, A_1)
c_1 = Segment(A_1, A_2)
d_1 = Segment(A_3, A_2)
e = Segment(A_3, A_4)
O_1: 0.5 * (A_1 + A_3)
r: 0.2 * Distance[A_1, A_2]
B_0: O_1 + (r, 0)
B_3: B_1
B_4: B_1
B_5: B_1
B_6: B_1
B_7: B_1
B_8: O_1 + (r * cos(240°), r * sin(240°))
B_9: O_1 + (r * cos(270°), r * sin(270°))
B_{10}: O_1 + (r * cos(300°), r * sin(300°))
B_{11}: O_1 + (r * cos(330°), r * sin(330°))
f = Line(B_3, B_9)
B_2: B_1
g = Line(B_2, B_8)
i = Line(B_1, B_7)
j = Line(B_0, B_6)
l = Line(B_4, B_{10})
m = Line(B_5, B_{11})
C_3 = Intersect(f, e)
C_2 = Intersect(g, e)
C_1 = Intersect(i, d_1)
C_0 = Intersect(j, d_1)
C_{11} = Intersect(m, d_1)
C_{10} = Intersect(l, c_1)
C_9 = Intersect(f, c_1)
C_8 = Intersect(g, c_1)
C_7 = Intersect(i, b_1)
C_5 = Intersect(m, b_1)
C_4 = Intersect(l, e)
C_6 = Intersect(j, b_1)
A = Midpoint(A_1, A_2)
B = Midpoint(A_2, A_3)
C = Midpoint(A_3, A_4)
D = Midpoint(A_4, A_1)
Q_1: O
Q_4: Q_1 + (0, L)
h = false
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
inputBox4 = Textfield(d)
k = true
u = Vector((-L - 2.3, 0), (L + 2.3, 0))
v = Vector((0, -L - 2.3), (0, L + 2.3))
text2: "\left [\begin{array}{cc} " + (LaTeX[a]) + " &" + (LaTeX[b]) + " \\" + (LaTeX[c]) + " &" + (LaTeX[d]) + " \\ \end{array}   \right ] \left [  \begin{array}{cc} x \\ y \\ \end{array} \right ] =\left [ \begin{array}{cc} " + (LaTeX[a]) + "x" + (LaTeX[If[b < 0, "-", "+"]]) + "" + (LaTeX[abs(b)]) + " y\\ " + (LaTeX[c]) + "x" + (LaTeX[If[d < 0, "-", "+"]]) + "" + (LaTeX[abs(d)]) + " y\\ \end{array}  \right ] "