Starting diary file "diary-2016-02-10.txt" on Wed Feb 10 2016 12:29 PM.
load midtermgrades
max(G)
ans =
98
sum(G == 98)
ans =
2
median(G)
ans =
82
mean(G)
ans =
78.0943
hist(G, 0:10:100)
clc
A = randn(4)
A =
-1.9184 0.0772 -1.8290 -0.2273
-0.1311 0.3756 2.0915 1.5938
-0.7686 0.3956 0.3591 0.1552
2.3900 -0.1125 -0.7943 0.1786
max(max(abs(A)))
ans =
2.3900
norm(A)
ans =
3.3650
norm(A,2)
ans =
3.3650
clear
clc
A = [2 -1 0 ; -1 2 -1 ; 0 -1 2]
A =
2 -1 0
-1 2 -1
0 -1 2
[V,D] = eig(A)
V =
-0.5000 -0.7071 0.5000
-0.7071 0.0000 -0.7071
-0.5000 0.7071 0.5000
D =
0.5858 0 0
0 2.0000 0
0 0 3.4142
v1 = V(:,1)
v1 =
-0.5000
-0.7071
-0.5000
v2 = V(:,2)
v2 =
-0.7071
0.0000
0.7071
A*v1
ans =
-0.2929
-0.4142
-0.2929
D(1,1)*v1
ans =
-0.2929
-0.4142
-0.2929
size(v1)
ans =
3 1
size(v2)
ans =
3 1
v1' * v2
ans =
2.2204e-16
V
V =
-0.5000 -0.7071 0.5000
-0.7071 0.0000 -0.7071
-0.5000 0.7071 0.5000
V'
ans =
-0.5000 -0.7071 -0.5000
-0.7071 0.0000 0.7071
0.5000 -0.7071 0.5000
V' * V
ans =
1.0000 0.0000 -0.0000
0.0000 1.0000 -0.0000
-0.0000 -0.0000 1.0000
V
V =
-0.5000 -0.7071 0.5000
-0.7071 0.0000 -0.7071
-0.5000 0.7071 0.5000
A*V - V* D
ans =
1.0e-15 *
-0.4441 -0.4441 0
0.3886 0.3747 -0.4441
0.1110 0 -0.2220
lambda = diag(D)
lambda =
0.5858
2.0000
3.4142
v1 = V(:,1)
v1 =
-0.5000
-0.7071
-0.5000
v2 = V(:,2)
v2 =
-0.7071
0.0000
0.7071
v3 = V(:,3)
v3 =
0.5000
-0.7071
0.5000
A1 = v1 * lambda(1) * v1'
A1 =
0.1464 0.2071 0.1464
0.2071 0.2929 0.2071
0.1464 0.2071 0.1464
A2 = v2 * lambda(2) * v2'
A2 =
1.0000 -0.0000 -1.0000
-0.0000 0.0000 0.0000
-1.0000 0.0000 1.0000
A3 = v3 * lambda(3) * v3'
A3 =
0.8536 -1.2071 0.8536
-1.2071 1.7071 -1.2071
0.8536 -1.2071 0.8536
A1+A2+A3
ans =
2.0000 -1.0000 0.0000
-1.0000 2.0000 -1.0000
0.0000 -1.0000 2.0000
A
A =
2 -1 0
-1 2 -1
0 -1 2
clc
clear
load temperature
whos
Name Size Bytes Class Attributes
A100 10000x10000 873608 double sparse
A4 16x16 2048 double
b100 10000x1 80000 double
b4 16x1 128 double
A = A4
A =
Columns 1 through 9
4 -1 0 0 -1 0 0 0 0
-1 4 -1 0 0 -1 0 0 0
0 -1 4 -1 0 0 -1 0 0
0 0 -1 4 0 0 0 -1 0
-1 0 0 0 4 -1 0 0 -1
0 -1 0 0 -1 4 -1 0 0
0 0 -1 0 0 -1 4 -1 0
0 0 0 -1 0 0 -1 4 0
0 0 0 0 -1 0 0 0 4
0 0 0 0 0 -1 0 0 -1
0 0 0 0 0 0 -1 0 0
0 0 0 0 0 0 0 -1 0
0 0 0 0 0 0 0 0 -1
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
Columns 10 through 16
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
-1 0 0 0 0 0 0
0 -1 0 0 0 0 0
0 0 -1 0 0 0 0
-1 0 0 -1 0 0 0
4 -1 0 0 -1 0 0
-1 4 -1 0 0 -1 0
0 -1 4 0 0 0 -1
0 0 0 4 -1 0 0
-1 0 0 -1 4 -1 0
0 -1 0 0 -1 4 -1
0 0 -1 0 0 -1 4
spy(A)
[V, D] =eig(A);
V
V =
...
diag(D)
ans =
0.7639
1.7639
1.7639
2.7639
3.0000
3.0000
4.0000
4.0000
4.0000
4.0000
5.0000
5.0000
5.2361
6.2361
6.2361
7.2361
spynum(A)
approximation(A)
clc
spy
S =spyimg;
size(S)
ans =
108 91
rank(S)
ans =
87
approximation(S)