- #1
Paul Shredder
- 3
- 0
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 Ax=0 (with dim(A)=n x n) is the vector x=0n x 1, means that A is of full rank and the rows and columns of the matrix are linearly independent.
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! :)
When you have a square matrix with empty null space, that is, the only solution to the equation Ax=0 (with dim(A)=n x n) is the vector x=0n x 1, means that A is of full rank and the rows and columns of the matrix are linearly independent.
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! :)