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## Main Question or Discussion Point

Hi all, i've occasionly seen people multiply a matrix by its transpose, what is the use and intuition of the product? Any help appreciated.

- Thread starter NotASmurf
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Hi all, i've occasionly seen people multiply a matrix by its transpose, what is the use and intuition of the product? Any help appreciated.

- #2

DrClaude

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Were these orthogonal matrices, where M^{-1} = M^{T}?

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In one case yes, What would that mean intuition wise?

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DrClaude

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In that case, its use is obvious, as M MIn one case yes,

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Was in stats, with covarience matrices.In that case, its use is obvious, as M M^{T}= I. Otherwise, it depends on the context.

- #6

Fredrik

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These products show up when inner products are involved. For example, if you write elements of ##\mathbb R^n## as n×1 matrices, you can write ##x\cdot y=x^Ty##. From this you get results like ##(Mx)\cdot(My)=(Mx)^T(My)=x^TM^TMy##.Hi all, i've occasionly seen people multiply a matrix by its transpose, what is the use and intuition of the product? Any help appreciated.

- #7

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The column vectors are orthonormal. Multiplying by the transpose makes you dot all the column vectors together with each other to get each entry of the product, which it the identity matrix.What would that mean intuition wise?

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