A = |
┌ a_{1} ┐ │ a_{2} │ └ a_{3} ┘ |
B = |
┌ b_{1} ┐ │ b_{2} │ └ b_{3} ┘ |
A + B = |
┌ a_{1} ┐ │ a_{2} │ └ a_{3} ┘ |
+ |
┌ b_{1} ┐ │ b_{2} │ └ b_{3} ┘ |
= |
┌ a_{1} + b_{1} ┐ │ a_{2} + b_{2} │ └ a_{3} + b_{3} ┘ |
= |
┌ b_{1} + a_{1} ┐ │ b_{2} + a_{2} │ └ b_{3} + a_{3} ┘ |
= |
B + A |
┌ a b ┐ └ c d ┘ |
┌ x ┐ └ y ┘ |
= |
┌ ax+by ┐ └ cx+dy ┘ |
= |
┌ x' ┐ └ y' ┘ |
┌ 3 0 ┐ └ 0 3 ┘ |
┌ 1 ┐ └ 2 ┘ |
= |
┌ 3*1+0*2 ┐ └ 0*2+3*2 ┘ |
= |
┌ 3 ┐ └ 6 ┘ |
┌ cos(ϕ). sin(ϕ) ┐ └ -sin(ϕ) cos(ϕ) ┘ |
┌ x ┐ └ y ┘ |
5 * |
┌ 3 ┐ └ 2 ┘ |
= |
┌ 15 ┐ └ 10 ┘ |
┌ a b ┐ └ c d ┘ |
┌ x ┐ └ y ┘ |
= |
┌ x' ┐ └ y' ┘ |
A = |
┌ a b ┐ └ c d ┘ |
λ A = |
┌ λa λb ┐ └ λc λd ┘ |
A = |
┌ a_{11} a_{12} a_{13} a_{14} ┐ └ a_{21} a_{22} a_{23} a_{24} ┘ |
B = |
┌ b_{11} b_{12} b_{13} b_{14} ┐ └ b_{21} b_{22} b_{23} b_{24} ┘ |
A + B = B + A= |
┌ a_{11}+b_{11} a_{12}+b_{12} a_{13}+b_{13} a_{14}+b_{14} ┐ └ a_{21}+b_{21} a_{22}+b_{22} a_{23}+b_{23} a_{24}+b_{24} ┘ |
I = |
┌ 1 0 0 ┐ │ 0 1 0 │ └ 0 0 1 ┘ |
I = |
┌ 1 0 ┐ └ 0 1 ┘ |
IX = |
┌ 1 0 0 ┐ │ 0 1 0 │ └ 0 0 1 ┘ |
┌ x ┐ │ y │ └ z ┘ |
= |
┌ 1x+0y+0z ┐ │ 0x+1y+0z │ └ 0x+0y+1z ┘ |
= |
┌ x ┐ │ y │ └ z ┘ |
A = |
┌ a_{11} a_{12} a_{13} ┐ │ a_{21} a_{22} a_{23} │ └ a_{31} a_{32} a_{33} ┘ |
┌ a_{11} ┐ │ a_{21} │ └ a_{31} ┘ |
, |
┌ a_{12} ┐ │ a_{22} │ └ a_{32} ┘ |
, |
┌ a_{13} ┐ │ a_{23} │ └ a_{33} ┘ |
A = |
┌ 2 1 0 ┐ └ 1 3 5 ┘ |
^{t}A = |
┌ 2 1 ┐ │ 1 3 │ └ 0 5 ┘ |
A = |
┌ 2 1 5┐ │ 1 3 0│ └ 5 0 2┘ |
A = |
┌ a b ┐ └ c d ┘ |
A = |
┌ 3 0 ┐ └ 0 3 ┘ |
B = |
┌ 1 2 ┐ └ 2 4 ┘ |
┌ 2 ┐ └ 4 ┘ |
= | 2* |
┌ 1 ┐ └ 2 ┘ |
A = |
┌ 0 -1 ┐ └ 1. 0 ┘ |
u = |
┌ 1 ┐ └ 0 ┘ |
v = |
┌ 0 ┐ └ 1 ┘ |
Aw = |
┌ 0 -1 ┐ └ 1. 0 ┘ |
┌ 1 ┐ └ 1 ┘ |
= |
┌ -1 ┐ └ 1. ┘ |
Au = |
┌ 0 -1 ┐ └ 1. 0 ┘ |
┌ 1 ┐ └ 0 ┘ |
= |
┌ 0 ┐ └ 1 ┘ |
Av = |
┌ 0 -1 ┐ └ 1. 0 ┘ |
┌ 0 ┐ └ 1 ┘ |
= |
┌ -1 ┐ └ 0. ┘ |
Au + Av = | Aw = |
┌ 0 ┐ └ 1 ┘ |
+ |
┌ -1 ┐ └ 0. ┘ |
= |
┌ -1 ┐ └ 1. ┘ |
F(E^{1})= |
┌ 2 ┐ └ 1 ┘ |
, | F(E^{2})= |
┌ 3. ┐ └ -1 ┘ |
, | F(E^{3})= |
┌ -5 ┐ └ 4. ┘ |
, | F(E^{4})= |
┌ 1 ┐ └ 7 ┘ |
F = |
┌ 2 3. -5 1 ┐ └ 1 -1 4. 7 ┘ |
F = |
┌ a b c ┐ │ d e f │ └ g h i ┘ |
┌ 1 ┐ │ 0 │ └ 0 ┘ |
, |
┌ 0 ┐ │ 1 │ └ 0 ┘ |
, |
┌ 0 ┐ │ 0 │ └ 1 ┘ |
┌ a b c ┐ │ d e f │ └ g h i ┘ |
┌ 1 ┐ │ 0 │ └ 0 ┘ |
= |
┌ a*1+b*0+c*0 ┐ │ d*1+e*0+f*0 │ └ g*1+h*0+i*0 ┘ |
= |
┌ a ┐ │ d │ └ g ┘ |
┌ x ┐ │ y │ └ z ┘ |
= | A + λ (B - A) |
┌ x ┐ │ y │ └ z ┘ |
= | C + μ (D - C) |
A + λ (B - A) | = | C + μ (D - C) |