substitute each element of a vector into a matrix without using loop

Hi I want to substitute each element of vector1 into 'x' in matrix1 and store each matrix in an array without using a loop. Please tell me how.

vector1=[1:1:10];
matrix1=[4*x 5*x ; 4*x 2*x];

Thanks in advance.

Answer 1

[Jan]

Like this?

 vector = 1:1:10;
 vector = reshape( vector, [1, 1, numel(vector)] ); 
 one_vector = ones( 1, 1, numel(vector) );
 matrix = [4 * vector, 5 * one_vector; 4 * one_vector, 2 * vector ];

[AllKindsofMath AllKinds]

Thank you that looks very good. But I don't understand what this line does

 vector = reshape( vector, [1, 1, numel(vector)] );

can you explain it please?

[Jan]

It forces vector to have the dimension [1, 1, numel(vector)]. I.e. if you will, the result is a 3D matrix with exactly one row, one column and numel(vector) elements in the third dimension.

[AllKindsofMath AllKinds]

Brilliant thank you!

[AllKindsofMath AllKinds]

Another question, I want to find the determinant of each matrix. So when I try det(matrix) it doesn't work, but with det(matrix(:,:,10)) for example it does. Can I apply 'det' to all elements of 'matrix'?

[Jan]

Not as far as I can see. You will probably have to iterate over the third dimension.

Answer 2

[Sean de Wolski]

So:

vector1=[1:1:10];
x = vector1;
matrix1=[4*x 5*x ; 4*x 2*x];

Or is x symbolic?

clear x;
syms x
matrix1=[4*x 5*x ; 4*x 2*x];
matrix1 = subs(matrix1,x,vector1)

[AllKindsofMath AllKinds]

x is symbolic so my example should really be something like

matrix1=[4*x 5 ; 4 2*x];

[Sean de Wolski]

i.e. the second half of what I have...

[AllKindsofMath AllKinds]

Yes but if I want the matrix for vector1(4) how do I display it?

[Sean de Wolski]

subs(matrix1,x,vector1(4))

[AllKindsofMath AllKinds]

Yeh but I want all of the matrices to be stored in an array so that I can call on them when I need them.

Answer 3

[Jan]

Maybe something like the following?

 matrix = [4, 5; 4, 2]; 
 [p, q] = size( matrix ); 
 vector = 1:1:10; 
 matrix = repmat( matrix(:), 1, numel( vector ) ); 
 matrix = matrix .* repmat( vector, p*q, 1 ); 
 matrix = reshape( matrix, p, q, numel( vector ) );

This gives you a 3d matrix, where each layer contains the specified matrix, mulitplied by one entry in vector

[AllKindsofMath AllKinds]

This is almost there! in my example I have each element multiplied by x, but this was probably misleading as each element will not be multiplied by x. So more like

matrix1 = [4*x 5 ; 4 2*x];

Answer 4

[Alfonso Nieto-Castanon]

perhaps something like:

 f = @(x)[4*x 5 ; 4 2*x];             % Matrix in functional form
 vector = 1:10;                       % Your vector of values for 'x'
 matrix = arrayfun(f,vector,'uni',0); % A cell array of matrices

 values = cellfun(@det,matrix);       % Determinant of each of those matrices