Can any one suggest me how to make a large matrics positive definate.

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shilpa 2015-5-27

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回答： Alfonso Nieto-Castanon 2015-5-27

I have matrices whose positive eigen values have to be calculated. In order to find them the matrices have to be positive definite. Kindly anyone suggest.

Can SDV be used for it? If yes then how?

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Answer 1

Walter Roberson 2015-5-27

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The trick is to use

pdmat = (YourMatrix + YourMatrix.')/2;

Or is the question to find out if a given matrix is positive definite? If so then note that the positive definite tests are very sensitive to the exact bit values of floating point numbers, so a matrix that looks positive definite might not be because of a single bit difference between two numbers. The above trick is routinely used on matrices that "should" be positive definite in order to force the last bits to be the same in the symmetric positions.

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John D'Errico 2015-5-27

编辑：John D'Errico 2015-5-27

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The above trick of averaging the matrix with its transpose will indeed suffice to make it symmetric. But a symmetric matrix can still have negative eigenvalues. There will be no complex eigenvalues.

A = -eye(5);

A is perfectly symmetric, yet not at all positive definite, and trying to make it so by symmetrizing it will not suffice.

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