% EVD_deriv--sent

close all;
clear all;
format compact;
format short;
warning off;

% SkaiWiD-wyklad#06'-sent.pdf
% -- 31
% -- 29
% -- 28
% (bez szczegolow dotyczacych istnienia/jednoznacznosci)

% macierz diagonalna
D = [1 0 0; 0 2 0; 0 0 3]

k = [3;2;1]
Dk = diag(k)

D*Dk
Dk*D

% mnozenie macierzy 

M = [0 1 2; 1 2 3; 2 3 4]

% (prawostronne) mnozenie przez wektor

k1 = [1;2;3]
k2 = [2;3;1]
k3 = [3;1;2]

[k1]
[k1 k2]
[k1 k2 k3]

M*k1
M*k2
M*k3

[M*k1]
[M*k1 M*k2]
[M*k1 M*k2 M*k3]

M*[k1 k2 k3]

% (prawostronne) mnozenie przez macierz diagonalna

M
k

M(:,1)*k(1)
M(:,2)*k(2)
M(:,3)*k(3)

[M(:,1)*k(1)  M(:,2)*k(2)  M(:,3)*k(3)]

Dk = diag(k)
M*Dk

% wartosci i wektory wlasne macierzy

A = [1 2 3;3 5 7;3 2 0]

[K,L] = eig(A)

A*K(:,1)
K(:,1)*L(1,1)

[A*K(:,1), K(:,1)*L(1,1)]
[A*K(:,2), K(:,2)*L(2,2)]
[A*K(:,3), K(:,3)*L(3,3)]


[A*K(:,1)  A*K(:,2)  A*K(:,3)]
A*K

[K(:,1)*L(1,1)  K(:,2)*L(2,2)  K(:,3)*L(3,3)]
K*L

A*K
K*L

% WSZEDZIE DALEJ ZAKLADAMY: K posiada odwrotnosc (w postaci inv(K) = K' lub tylko inv(K))

K
det(K)
inv(K)
K*inv(K)

% A*K = K*L
% A*K*inv(K) = K*L*inv(K)
% A = K*L*inv(K)

A
K*L*inv(K)

K
det(K)
inv(K)
K'
K*inv(K)
K*K'

K*L*K'


A = [19    23    24; 23    33    41; 24    41    58]

[K,L] = eig(A)

A*K
K*L

K
det(K)
inv(K)
K*inv(K)

A
K*L*inv(K)

K
det(K)
inv(K)
K'
K*inv(K)
K*K'

K*L*K'