Page 51 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

and column j of is the entry in row j and column i of A; that is,
(11)

Note the reversal of the subscripts.
In the special case where A is a square matrix, the transpose of A can be obtained by interchanging entries that are
symmetrically positioned about the main diagonal. In 12 it is shown that can also be obtained by “reflecting” A about its
main diagonal.

(12)

DEFINITION
If A is a square matrix, then the trace of A, denoted by , is defined to be the sum of the entries on the main diagonal
of A. The trace of A is undefined if A is not a square matrix.

EXAMPLE 12 Trace of a Matrix
The following are examples of matrices and their traces.

Exercise Set 1.3

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Suppose that A, B, C, D, and E are matrices with the following sizes:
1.