1. Jan 28, 2015 #1

   NotASmurf

   

   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.

    

   NotASmurf, Jan 28, 2015
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3. Jan 29, 2015 #2

   DrClaude

   

   Staff: Mentor

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

    

   DrClaude, Jan 29, 2015
4. Jan 29, 2015 #3

   NotASmurf

   

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

    

   NotASmurf, Jan 29, 2015
5. Jan 29, 2015 #4

   DrClaude

   

   Staff: Mentor

   In that case, its use is obvious, as M M^T = I. Otherwise, it depends on the context.

    

   DrClaude, Jan 29, 2015
6. Jan 29, 2015 #5

   NotASmurf

   

   Was in stats, with covarience matrices.

    

   NotASmurf, Jan 29, 2015
7. Jan 29, 2015 #6

   Fredrik

   

   Staff Emeritus

   Science Advisor

   Gold Member

   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##.

    

   Fredrik, Jan 29, 2015
8. Jan 30, 2015 #7

   homeomorphic

   

   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.

    

   homeomorphic, Jan 30, 2015

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