Continuing basic definitions… If is an (i.e., a matrix), then n-vector n1 . Let be a with all zeroes except the component, which is 1. Then ei n-vector ith = [ ] I e1, e2, en …, is the identity matrix. Further, if is then nn A nn, IA=AI=A. The matrix is said to be if ! such that nn A nonsingular x Ax=b, b. Tests for nonsingularity:
Continuing basic definitions… If is an n-vector (i.e., a n1 matrix), then . Let ei be a n-vector with all zeroes except the ith component, which is 1. Then I = [ e1, e2, …, en ] is the nn identity matrix. Further, if A is nn, then IA=AI=A. The nn matrix A is said to be nonsingular if ! x such that Ax=b, b. Tests for nonsingularity:
2013sw.docx