MATH136 Chapter Notes - Chapter 69-102: Rotation Matrix, Identity Function, Row And Column Spaces

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Dan Wolczuk

Document Summary

An m n matrix a is a rectangular array with m rows and n columns. We denote the entry in the i-th row and j-th column by aij. The set of all m n matrices with real entries is denoted by mm n(r). Let a, b mm n(r) and c r. we de ne a + b and ca by (a + b)ij = (a)ij + (b)ij (ca)ij = c (a)ij (1) (2) (3) 0m,n is de ned by (0m,n)ij = 0: there exists a matrix ( a) mm n(r) such that a + ( a) = 0m,n. In particular, ( a) is de ned by ( a)ij = (a)ij: ca mm n(r, c(da) = (cd)a, (c + d)a = ca + da, c(a + b) = ca + cb, 1a = a. The transpose of an m n matrix a is the n m matrix at whose ij-th entry is the ji-th entry of a.