mws_gen_sle_bck_unary

mws_gen_sle_bck_unary - Chapter 04.04 Unary Matrix...

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04.04.1 Chapter 04.04 Unary Matrix Operations After reading this chapter, you should be able to: 1. know what unary operations means, 2. find the transpose of a square matrix and it’s relationship to symmetric matrices, 3. find the trace of a matrix, and 4. find the determinant of a matrix by the cofactor method. What is the transpose of a matrix? Let ] [ A be a n m × matrix. Then ] [ B is the transpose of the ] [ A if ij ij a b = for all i and j . That is, the th i row and the th j column element of ] [ A is the th j row and th i column element of ] [ B . Note, ] [ B would be a m n × matrix. The transpose of ] [ A is denoted by T ] [ A . Example 1 Find the transpose of = 27 7 16 6 25 15 10 5 2 3 20 25 ] [ A Solution The transpose of ] [ A is [ ] = 27 25 2 7 15 3 16 10 20 6 5 25 T A Note, the transpose of a row vector is a column vector and the transpose of a column vector is a row vector. Also, note that the transpose of a transpose of a matrix is the matrix itself, that is, [ ] ( ) [ ] A A = T T . Also, ( ) ( ) T T T T T ; cA cA B A B A = + = + .
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