Matlab function that takes in a matrix to test for positive definite

Write a matlab function that takes in a matrix to test for positive definite.

[Steven Lord]

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Answer 1

[Kautuk Raj]

This is a MATLAB function that tests whether a given matrix is positive definite:

function [is_pd] = isPositiveDefinite(A)
% Function to test whether a matrix is positive definite
% Input: A - the matrix to test
% Output: is_pd - a boolean indicating whether A is positive definite
% Check that A is square
if size(A,1) ~= size(A,2)
    error('Matrix must be square');
end
% Check that A is symmetric
if ~isequal(A, A')
    error('Matrix must be symmetric');
end
% Compute the eigenvalues of A
lambda = eig(A);
% Check that all eigenvalues are positive
is_pd = all(lambda > 0);
end

An example of how to use the function:

% Test matrix
A = [4 1 2; 1 5 3; 2 3 6];
% Check if A is positive definite
is_pd = isPositiveDefinite(A);
% Display result
if is_pd
    disp('A is positive definite');
else
    disp('A is not positive definite');
end