null space of a matrix in matlab

To find the null space of a matrix in MATLAB, you can use the null function. Here's an example of how to use it:

main.m
A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; % example matrix
null_space = null(A); % compute the null space
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The null function returns a matrix whose columns form a basis for the null space of the input matrix A. Each column corresponds to a different vector in the null space.

You can also specify a tolerance level for finding the null space vectors by adding a second argument to the null function. For example:

main.m
null_space = null(A, 1e-6); % specify a tolerance of 1e-6
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This can be useful if you want to consider vectors that are close to zero as part of the null space.

Note that the null space will be returned as a matrix in MATLAB, even if it contains only one vector. If you want to extract the individual null space vectors, you can do so using indexing. For example, null_space(:, 1) will give you the first vector in the null space.

Hope this helps!