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## Main Question or Discussion Point

Hi guys, I hope you are having a great day, this is Paul and, as you have seen in the title, that's what I'm looking for, let me explain:

When you have a square matrix with empty null space, that is, the only solution to the equation

The question is:

For example, particular cases are the identity matrix, upper and lower diagonal matrices. But I need to find

Sounds crazy, because there are a lot of posibilities, and I do not expect you to solve me the complete problem (but if you do, it would be really great, hahaha), but I would like you to suggest me about some bibliography where I can find any clue to solve this problem.

I already read some Linear Algebra books, but I only found the basics of the issue, that is, the concept of Null Space, orthogonal complement to row space of A, and that kind of stuff.

Well, sorry if I wrote too many lines, but it was for a good explaining of the issue. Haha.

Thanks for reading and answering, I send you greetings from México, goodbye guys! :)

When you have a square matrix with empty null space, that is, the only solution to the equation

*(with***Ax=0***) is the vector***dim(A)=n x n****x=0**_{n x 1}, means that*is of full rank and the rows and columns of the matrix are linearly independent.***A**The question is:

**What structure does***A*must have to accomplish this requeriment?For example, particular cases are the identity matrix, upper and lower diagonal matrices. But I need to find

**ALL THE POSIBILITIES FOR ALL SIZES OF MATRICES!!!**Sounds crazy, because there are a lot of posibilities, and I do not expect you to solve me the complete problem (but if you do, it would be really great, hahaha), but I would like you to suggest me about some bibliography where I can find any clue to solve this problem.

I already read some Linear Algebra books, but I only found the basics of the issue, that is, the concept of Null Space, orthogonal complement to row space of A, and that kind of stuff.

Well, sorry if I wrote too many lines, but it was for a good explaining of the issue. Haha.

Thanks for reading and answering, I send you greetings from México, goodbye guys! :)