If the scalar product is non degenerate then the metric matrix is invertible and symmetric : why?
39334
Non-degenerate bilinear forms and invertible matrices
3408
Do positive semidefinite matrices have to be symmetric?
75066
If the product of two square matrices is invertible, then both matrices are invertible
116136
Proof that the inverse of a square matrix is unique
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
10042
How to Show that Linear transformation is invertible?
129704
Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism?
70289
What does a symmetric matrix transformation do, geometrically?
8970
Proving the cross product matrix tranformation identity with an alternative solution
54628
Properties of non-zero symmetric bilinear form
89649
Linear Algebra munkres analysis on manifolds question.
93835
Why do those terms vanish if the metric is Hermitian?
131701
Why is $A^TA$ invertible if $A$ has independent columns?
114208
Does non-symmetric positive definite matrix have positive eigenvalues?
66995
Why is a projection matrix symmetric?
103665
Product of matrices of different order is not invertible
75391
How to prove that a left-invariant metric on a Lie group is smooth?