I have learnt that the intuitive idea behind inner product space is finding angles between vectors. But what does inner product actually mean physically or intuitively when it comes to matrices.Can I link inner product of matrices to concept of angles?.I can't imagine angles between matrices as I do for vectors. I really want to learn visually and not just theoretically. As I am amateur in this area my understanding might be wrong. So please do correct me.

  • 2
    $\begingroup$ A matrix is actually a vector (put all matrix entries in one column. Matrices form a vector space, so the elements are vectors). So you can use your "intuition" with inner product of vectors. $\endgroup$ Aug 11, 2023 at 17:35
  • $\begingroup$ Are you defining the inner product of two matrices as $\boldsymbol{A}^\intercal \boldsymbol{B}$ ? $\endgroup$ Aug 11, 2023 at 18:09


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