Are there some test to know if a matrix $M$ is gramian ? $M$ is gramian if it exists a matrix W such $M=W^HW$. Also if it is possible to determine $W$.
Thanks
2026-04-12 03:30:35.1775964635
Gramian matrix test
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Gramian matrix is positive-definite. So it's possible to find square root. It will be symmetrical so this it is possible to write such decomposition for any positive definite matrix. The solution of $M=WW^{T}$ it is not unique, because starting from nonsymmetric matrix $A$ one can construct matrix $B=AA^T$ and then a symmetric solution of $B=WW^T$.