(2 x 3) matrix is defined by
a11 a12 a13
A=
a21 a22 a23
Then the transpose of A, denoted by A’, is now (3 x 2)
a11
A′ = a12
a13
•
•
a 21
a22
a 23
( A′)′ = A
(kA)′ = kA′ , where k is a scalar.
SYMMETRIC M ATRIX
When A′ = A , the matrix is called symmetric. That is, a symmetric matrix is a square matrix, in that it
has the same number of rows as it has columns, and the off-diagonal elements are symmetric (i.e.
a ij = a ji for all i and j ).
For example,
4 5 − 3
A =…
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