I work on a project, for these project i need to generate a square random invertible matrix.
I found out how to generate a square random matrix, still i want to be sure that this is an invertible one, without having to compute the determinant or to generate this matrix multiple times, can you please give me a tip ?
A mean to be sure that a matrix has nonzero determinant is to take it as diagonally dominant (say for example on each column $j$, $|a_{jj}|> \sum_{i=1...n, i \neq j}|a_{ij}|$) https://en.wikipedia.org/wiki/Diagonally_dominant_matrix It can be also done on rows.