Intuition & use of M*M^T product of matrix & its transpose?

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.

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DrClaude
Mentor
Were these orthogonal matrices, where M-1 = MT?

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

DrClaude
Mentor
In one case yes,
In that case, its use is obvious, as M MT = I. Otherwise, it depends on the context.

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

Fredrik
Staff Emeritus
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 $(Mx)\cdot(My)=(Mx)^T(My)=x^TM^TMy$.