Page 511 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

498 Determinants and Matrices Appen. C

C.2 MATRICES
Matrix. A rectangular array of terms arranged in m rows and n columns is
called a matrix. For example,
■«II «12 ^13 «14
A = «21 «22 ^23 «24
«31 «32 «33 «34
is a 3 X 4 matrix.
Square matrix. A square matrix is one in which the number of rows is
equal to the number of columns. It is referred to as an X n matrix or a matrbc of
order n.

Symmetric matrix. A square matrix is said to be symmetric if the elements
on the upper right half can be obtained by flipping the matrix about the diagonal.
2 1 3
A = 1 5 0 = symmetric matrix
3 0 1

Trace. The sum of the diagonal elements of a square matrix is called the
trace. For the previous matrk,
Trace ^ = 2 + 5 + l = 8

Singular matrix. If the determinant of a matrix is zero, the matrix is said
to be singular.
Row matrix. A row matrix has m = 1.

[
]
B =b^ ¿ 2 b^
Column matrix. A column matrix has n = 1.
'C ,

Zero matrix. The zero matrix is defined as one in which all elements are
zero.
0 0 0
0 =
0 0 0