MATLAB Matrices - Arizona State University



MATLAB Matrices

ways to create a matrix

1. type in matrix

[1-3,7;2,4,8]

1-3 7

2 4 8

2. zeros(N)

NxN matrix containing all zeros

3. rand(N)

NxN matrix of random numbers

4. randn(N)

NxN matrix of random numbers (positive and negative)

5. ones(N)

NxN matrix containig all ones

6. size(n)

will create a 1x2 matrix and tell the size of matrix “n”

7. diag(A)

lists the elements in the diagonal of matrix “A”

diag(A,k) lists the elements of the k-th diagonal

0.9047 0.4940 0.5007 0.4644

0.5045 0.2661 0.3841 0.9410

0.5163 0.0907 0.2771 0.0501

0.3190 0.9478 0.9138 0.7615

0.9866 0.0737 0.5297 0.7702

diag(a,2) 0.4940

diag(a) 0.1665

8. flipud(A)

flips the columns in matrix “A”

A =

0.6793 0.5194

0.9347 0.8310

0.3835 0.0346

» flipud(A)

ans =

0.3835 0.0346

0.9347 0.8310

0.6793 0.5194

9. fliplr(A)

flips rows in matrix “A”

A =

0.6793 0.5194

0.9347 0.8310

0.3835 0.0346

fliplr(A)

0.6793 0.2190

0.9347 0.0470

0.3835 0.6789

10. reshape(A,m,n)

rearranges matrix A to an mxn matrix

A =

2 3 13

11 10 8

7 6 12

14 15 1

reshape(A,8,2)

3

10

6

15

13

8

12

1

11. rot90

rotates matrix 90 degrees

rot90(N) rotates “N” ccw 90 degrees

rot90(N,k) rotates “N” ccw by k*90 degrees - k must be an integer

12. hankel

a matrix that is symmetric about and constant across the anti-diagonals

hankel(c) first column is c and ele below first anti-diag are zero

hankel(2:5)

ans =

3 4 5

4 5 0

5 0 0

0 0 0

13. hankel(c, r) first column is c and last row is r, if last of c and first of are differ, c wins

r=7:10;

hankel(c,r)

Column wins anti-diagonal conflict.

ans =

2 3 8

3 8 9

8 9 10

14. magic(N)

NxN matrix - a magic square, all rows and columns add to the same number

15. toeplitz

generates a toeplitz matrix given just the row or column description

toeplitz(c) symmetric matrix formed from vector “c”

[1:1:5];

toeplitz(c)

2 3 4 5

1 2 3 4

2 1 2 3

3 2 1 2

4 3 2 1

16. toeplitz(c,r)non-symm where c is first column and r is first row

[1.5:1:5.5];

[1:1:5];

toeplitz(c,r)

Column wins diagonal conflict.

2.5000 3.5000 4.5000 5.5000

1.0000 2.5000 3.5000 4.5000

2.0000 1.0000 2.5000 3.5000

3.0000 2.0000 1.0000 2.5000

4.0000 3.0000 2.0000 1.0000

17. compan(p)

companion matrix whose first row is -p(2:n)/p(1) -

[10 30 -70 60] - represents the polynomial 10x^3 + 30x^2 - 70x + 60

compan(p) (see also :”characteristic polynomial”)

7 -6

0 0

1 0

18. hadamard(N)

a Hadamard matrix of order N - a hadamard matrix is a matrix with 1’s and -1’s whose columns are orthogonal

hadamard(4)

1 1 1

-1 1 -1

1 -1 -1

-1 -1 1

19. meshgrid(x,y)

takes a vector and makes it an array (list of number) that can be plotted on a 3-D plot.

To eval and plot the function z=x^2+y^2

=meshgrid(-2:.2:2);

mesh(z)

20. forloop

programming tool which repeats an algorithm n number of times.

for i:n;

forj:n

=i^2+j^2

end

end

21. pascal(N)

PASCAL(N) is the Pascal matrix of order N: a symmetric positive

definite matrix with integer entries, made up from Pascal's

triangle. Its inverse has integer entries.

PASCAL(N,1) is the lower triangular Cholesky factor (up to signs

of columns) of the Pascal matrix. It is involutary (is its own

inverse).

PASCAL(N,2) is a transposed and permuted version of PASCAL(N,1)

which is a cube root of the identity.(from help pascal on MATLAB)

22. vander(N)

Vandermonde matrix.

VANDER(N) returns the Vandermonde matrix whose second to

last column is N. The j-th column of a Vandermonde

matrix is given by A(:,j) = N^(n-j).

For other matrices see hilb, invhilb, rosser,wilkinson

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