Matrix Alalysis, Matrix Algebra, Linear Algebra, what's the difference?

nn0p

Matrix Alalysis, Matrix Algebra, Linear Algebra, they seem to cover many similar topics.

Would someone explain about what are the differences between them?

Thanks in advance.

Stephen Tashi

Linear algebra is focused on vector spaces. Linear transformations between vector spaces can be represented by matrices so linear algebra emphasizes matrices in that context.

It's possible to study matrices simply as arrays of numbers without emphasizing that they represent linear transformations and I have seen books like that. They were mainly designed for non-mathematicians who needed to a little about matrices for some application, such as statistics or linear programming. However, I don't know whether to call such an approach "matrix analysis" or "matrix algebra". Did you have specific books with those titles in mind?

Special types of matrices and special ways to factor matrices into simpler types of matrices are studied in physics and applied mathematics. This could also be called "matrix analysis" or "matrix algebra". These would be topics a person normally studies only after taking an introductory course in Linear Algebra.