Dec 15, 2013 · The algebraic one: The set of invertible matrices is open (and non-empty) for the Zariski topology; explicitly, this means that there is a polynomial defined on the coefficients of the matrices, …

Apr 28, 2016 · I know that the product matrix of two invertible matrices must be invertible as well, but I am not sure how to prove that. I am trying to show it through the product of determinants if possible.

Mar 14, 2016 · The following presentation briefly explains the connection of these vector fields with invertible matrix subspace: Rachel Quinlan, Special spaces of matrices, IMS Meeting 2013, NUI …

The set of invertible matrices form a Zariski (dense) open subset, and hence to verify a polynomial identity, it suffices to verify it on this dense subset. Could someone provide an explanation of what it …

Nov 15, 2017 · Is there any intuitive relation or theorem between 'invertible' and 'diagonalizable'? Not directly, in the sense that one would imply another. You can have matrices in all four classes, i.e. …

How can we prove that all change-of-basis matrices are invertible? The trivial case when it's a change of basis for $\\mathbb{R^{n}}$ is easily demonstratable using, for example, determinants. But I...

Where in the history of linear algebra did we pick up on referring to invertible matrices as 'non-singular'? In fact, since the null space of an invertible matrix has a single vector an invertible

I am unsure how to go about doing this inverse product problem: The question says to find the value of each matrix expression where A and B are the invertible 3 x 3 matrices such that $$A^ {-1} = ...

May 20, 2018 · Basically same as GF (2) field but with different number. Let $\ \mathbf M_ {2 \times 2} (\mathbb Z_p) $ group of matrices and I need to find the number of invertible matrices in that group. I …

Oct 2, 2024 · The criteria for when a matrix reduces to the identity can be expressed in a number of ways (invertible matrices, determinants, columns being linearly independent, etc.).