[feature] Add more base routines for `stdlib_linalg`

[zoziha]

Description

Fortran has its unique grammatical characteristics. I think it is impossible to learn from some routines of Matlab and Python completely. We should be based on the characteristics of Fortran. Seeing the implementation of linspace/logspace in stdlib_math, I want to implement some routines in stdlib, mainly for stdlib_linalg.

Tasks

• [x] zeros (see #478)
• [x] ones (see #478)
• [x] seq/arange (see #480)
• [x] eye, for matrix is not square. (see #481)
• [ ] det (need BLAS #450 )
• [x] diff (see #605 )

---

• [x] is_square
• [x] is_symmetric

Prior Art

Some routines has been implemented in keurfonluu/Forlab (MIT license). I will rethink how to adapt to Fortran to write code.

[ghbrown]

I was thinking about proposing and implementing some matrix property checks like

• is_square (not sure if it's the same is is_squared?)
• is_symmetric
• is_triangular (upper, lower, and diagonal can fit in here somewhere)
• is_hermitian
• is_hessenberg (upper, lower, etc.) etc.

I think there is at least a little bit about API to discuss here, since for example I have found it very useful for is_square to also set the dimension n. Also, there should be a very clean way to set the API for checks that can result in upper/lower/diagonal/none, but we could discuss what is best for everyone.

I can open an issue to discuss this if that works for you.