18.2 Some special matrices 503
and the sum of the diagonal elements of the matrix, called the trace(or sometimes
spur) of the matrix,
(18.15)
EXAMPLE 18.2Find the determinant and trace of the matrix
By Example 17.6, the determinant of Ais
The trace of Ais
tr A 1 = 121 + 1 (−2) 1 + 101 + 1 (−1) 1 = 1 − 1
0 Exercises 3–6
Vectors
A matrix containing a single column only is called a column matrixor column vector;
a matrix containing one row only is a row matrixor row vector. The elements of a
vector are called components. Although matrices are normally denoted by uppercase
boldface letters, vectors are denoted by lowercase letters;
(18.16)
(only the single subscript is required for the components of a vector). Matrix algebra
includes vector algebra as a special case.
ab=,=
()aaa a
b
b
b
b
nn123123detA=
−
−
−
=−
2113
4201
1102
0311
16
A=
−
−
−
2113
4201
1102
0311
trA=+ +++ =
=∑
aaa a a
nnin11 22 33 ii1