Computing Data (Octave)

Matrices

1. A = [1 2; 3 4; 5 6]
$A=\begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}$
B = [11 12; 13 14; 15 16]
$B=\begin{pmatrix} 11 & 12 \\ 13 & 14 \\ 15 & 16 \end{pmatrix}$
C = [1 1; 2 2]
$C=\begin{pmatrix} 1 & 1 \\ 1 & 2 \end{pmatrix}$

2. A*C
$\begin{pmatrix} 5 & 5\\ 11 & 11 \\ 17 & 17 \end{pmatrix}$

3. A .* B take each element of A to multiply by each element of B
$\begin{pmatrix} 11 & 24\\ 39 & 56 \\ 75 & 96 \end{pmatrix}$

4. A .^ 2 square each element of A
$\begin{pmatrix} 1 & 4\\ 9 & 16 \\ 25 & 36 \end{pmatrix}$

5. v = [1; 2; 3]
$v=\begin{pmatrix} 1\\ 2\\ 3 \end{pmatrix}$

6. 1 ./ v element-wise reciprocal of v
$v=\begin{pmatrix} 1.00000\\ 0.50000\\ 0.33333 \end{pmatrix}$

7. log(v) element-wise logarithm of v
exp(v) element-wise exponential of v
abs(v) element-wise absolute value of v
-v element-wise negative value of v
v+1 element-wise addition of 1 to v

8. A = [1 2; 3 4; 5 6]
$A=\begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}$
A' transpose of A
$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}$

9. w = [1 15 2 0.5]
$w=\begin{pmatrix} 1 & 15 & 2 & 0.5 \end{pmatrix}$

10. max (w) maximum value of w
val = 15

11. [val, ind] = max(w) maximum value of w and index where it is located
val = 15
ind = 2

12. w < 3 element-wise comparison of whether w is less than 3
$\begin{pmatrix} 1 & 0 & 1 & 1 \end{pmatrix}$

13. find(w < 3) find which elements that variable w is less than 3
$\begin{pmatrix} 1 & 3 & 4 \end{pmatrix}$

14. sum(w) sum of w
ans = 18.5

15. prod(w) product of w
ans = 15

16. floor(w) rounds down elements of w
$\begin{pmatrix} 1 & 15 & 2 & 0 \end{pmatrix}$

17. ceil(w) rounds down elements of w
$\begin{pmatrix} 1 & 15 & 2 & 1 \end{pmatrix}$

18. A = magic(3) magic square of 3 by 3
$\begin{pmatrix} 8 & 1 & 6\\ 3 & 5 & 7\\ 4 & 9 & 2 \end{pmatrix}$

19. [r,c] = find(A >= 7) find rows and columns of A greater than or equal to 7
$r=\begin{pmatrix} 1\\ 3\\ 2 \end{pmatrix}$
$c=\begin{pmatrix} 1\\ 2\\ 3 \end{pmatrix}$

20. A(2,3)
$\begin{pmatrix} 7 \end{pmatrix}$

21. max(A,[],1) column-wise maximum of A
$\begin{pmatrix} 8 & 9 & 7 \end{pmatrix}$

22. max(A,[],2) row-wise maximum of A
$\begin{pmatrix} 8 \\ 7 \\ 9 \end{pmatrix}$

23. max(max(A))
$\begin{pmatrix} 9 \end{pmatrix}$

24. pinv(A) inverse of A
$\begin{pmatrix} 0.147 & -0.144 & 0.064 \\ -0.061 & 0.022 & 0.106 \\ -0.019 & 0.189 & -0.103 \end{pmatrix}$

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