>> A = [1 2; 3 4; 5 6]
A =
1 2
3 4
5 6
>> B = [11 12; 13 14; 15 16]
B =
11 12
13 14
15 16
>> c = [1 1; 2 2]
c =
1 1
2 2
>>%% matrix operations
>> A*B
error: operator *: nonconformant arguments (op1 is 3x2, op2 is 3x2)
>> C = [1 1; 2 2]
C =
1 1
2 2
>> A*C % matrix multiplication
ans =
5 5
11 11
17 17
>> A .* B % element-wise multiplcation A(i,i)*B(i,i)
% A .* C or A * B gives error - wrong dimensions
ans =
11 24
39 56
75 96
>> A .^ 2 % element-wise square of each element in A
ans =
1 4
9 16
25 36
>> v = [1; 2; 3]
v =
1
2
3
>> 1 ./ v % element-wise reciprocal
ans =
1.00000
0.50000
0.33333
>> 1 ./ A
ans =
1.00000 0.50000
0.33333 0.25000
0.20000 0.16667
>> log(v) % functions like this operate element-wise on vecs or matrices
ans =
0.00000
0.69315
1.09861
>> exp(v)
ans =
2.7183
7.3891
20.0855
>> v
v =
1
2
3
>> abs(v)
ans =
1
2
3
>> abs([-1; 2; -3])
ans =
1
2
3
>> -v % -1*v
ans =
-1
-2
-3
>> -1 * v
ans =
-1
-2
-3
>> v + ones(length(v),1) % v + 1
ans =
2
3
4
>> length(v)
ans = 3
>> v + 1
ans =
2
3
4
>> A
A =
1 2
3 4
5 6
>> A' % matrix transpose
ans =
1 3 5
2 4 6
>> (A')'
ans =
1 2
3 4
5 6
>>%% misc useful functions
>> a = [1 15 2 0.5]
a =
1.00000 15.00000 2.00000 0.50000
>> val = max(a)
val = 15
>> [val, ind] = max(a) % val - maximum element of the vector a and index - index value where maximum occur
val = 15
ind = 2
>> max(A) % if A is matrix, returns max from each column
ans =
5 6
>> a
a =
1.00000 15.00000 2.00000 0.50000
>> a < 3
ans =
1 0 1 1
>> find(a < 3)
ans =
1 3 4
>> A = magic(3)
A =
8 1 6
3 5 7
4 9 2
>> [r,c ] = find(A > 7)
r =
1
3
c =
1
2
>> [r,c ] = find(A >= 7) % row, column indices for values matching comparison
r =
1
3
2
c =
1
2
3
>>% sum, prod
>> a
a =
1.00000 15.00000 2.00000 0.50000
>> sum(a)
ans = 18.500
>> prod(a)
ans = 15
>> floor(a)
ans =
1 15 2 0
>> ceil(a)
ans =
1 15 2 1
>> rand(3)
ans =
0.31868 0.91598 0.51921
0.96554 0.27133 0.35385
0.42620 0.32065 0.18019
>> max(rand(3), rand(3))
ans =
0.46646 0.97470 0.11691
0.96954 0.98368 0.91132
0.56436 0.16409 0.55678
>> A
A =
8 1 6
3 5 7
4 9 2
>> max(A, [], 1)
ans =
8 9 7
>> max(A, [], 2)
ans =
8
7
9
>> max(A)
ans =
8 9 7
>> max(max(A))
ans = 9
>> A(:)
ans =
8
3
4
1
5
9
6
7
2
>> max(A(:))
ans = 9
>> A = magic(9)
A =
47 58 69 80 1 12 23 34 45
57 68 79 9 11 22 33 44 46
67 78 8 10 21 32 43 54 56
77 7 18 20 31 42 53 55 66
6 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 5
26 28 39 50 61 72 74 4 15
36 38 49 60 71 73 3 14 25
37 48 59 70 81 2 13 24 35
>> sum(A,1)
ans =
369 369 369 369 369 369 369 369 369
>> sum(A,2)
ans =
369
369
369
369
369
369
369
369
369
>> eye(9)
>>
>> eye(9)
>> A .* eye(9)
ans =
47 0 0 0 0 0 0 0 0
0 68 0 0 0 0 0 0 0
0 0 8 0 0 0 0 0 0
0 0 0 20 0 0 0 0 0
0 0 0 0 41 0 0 0 0
0 0 0 0 0 62 0 0 0
0 0 0 0 0 0 74 0 0
0 0 0 0 0 0 0 14 0
0 0 0 0 0 0 0 0 35
>> sum(sum(A.*eye(9)))
ans = 369
>> sum(sum(A.*flipup(eye(9))))
error: `flipup' undefined near line 127 column 12
error: evaluating argument list element number 1
error: evaluating argument list element number 1
error: evaluating argument list element number 1
error: evaluating argument list element number 1
>> sum(sum(A.*flipud(eye(9))))
ans = 369
>> flipud(eye(9))
>> A = magic(3)
A =
8 1 6
3 5 7
4 9 2
>>% Matrix inverse (pseudo-inverse)
>> pinv(A) % inv(A'*A)*A'
ans =
0.147222 -0.144444 0.063889
-0.061111 0.022222 0.105556
-0.019444 0.188889 -0.102778
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