INTRODUCTION OF LINEAR ALGEBRA AND ITS APPLICATIONS :
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences.
Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
Determinants are much further from the center of linear algebra than they were a hundred years ago. Mathematics keeps changing direction! After all, a single number can tell only so much about a matrix. Still, it is amazing how much this number can do. One viewpoint is this:
The determinant provides an explicit “formula” for each entry of A^−1 and A^−1b. This formula will not change the way we compute; even the determinant itself is found by elimination. In fact, elimination can be regarded as the most efficient way to substitute the entries of an n by n matrix into the formula. What the formula does is to show how A^−1 depends on the n^2 entries of A, and how it varies when those entries vary.