Classification,+Comparison+and+contrast+-+Version+1+with+classmate+comments

Clasification: (classification:) Matrix can be divided in a lot of groups depending on their properties, it ´ s dificult to create disjoint Partition of the matrix set. the first two big groups we can talk about are the singular and nonsingular matrix, singular matrix are those wich has an inverse, and non-singular are those who don ´ t.

Inside the singular matrix subset we can find a lot of subgroups such as: -Uper (upper) triangular matrix. -Lower triangular matrix. -Diagonal matrix, among others.

Inside the non-singular matrix we can find the following subsets: - The matrix wich has left inverse. - The matrixs (without s) wich has right inverse. - Those who don ´ t have ethir of them. (remenber that invertible matrix must have right and left inverse).

Comparing this two subset (subsets) of the matrix spaces can ilustrate the real diference between them:

-For example diagonal matrix from a computational point of view are easy to operate with, since they are mostly formed by 0, in the case of the non-singular matrix usually before using any kind of operations in them the computer must check its size since you dont have garatie of its elements using any properties over them can result in a lot of computational time.

-From a teorical point of view there are many case in wich you dont really have to know the exact solution of a system of equation, you just have to know that there exist, if u (you) have the garatie that the matrix is invertible you know that the system has an unique solution, in the set of the non-singular matrix you can ´ t say for certain if the system has a solution.