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- Thread starter NotASmurf
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DrClaude

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

- #3

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

- #4

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##.

- #7

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What would that mean intuition wise?

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.

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