The Engineering Handbook - Linear Algebra Matrices.pdf

Cain, G. “Linear Algebra Matrices”

The Engineering Handbook.

Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000



















































© 1998 by CRC PRESS LLC
197


Linear Algebra Matrices



Basic Definitions
Algebra of Matrices
Systems of Equations
Vector Spaces

Rank and Nullity
Orthogonality and Length
Determinants
Eigenvalues and Eigenvectors


e Cain
ia Institute of Technology



Basic Definitions

A matrix A is a rectangular array of numbers (real plex):

2 3
a a a
11 12 ¢ ¢ ¢ 1m
6 a21 a22 a2m 7
A = 6 ¢ ¢ ¢ 7
4 . 5
.
an1 an2 anm
¢ ¢ ¢

The size of the matrix is said to be n m . The 1 m matrices [a a a ] are called
£ £ i1 i2 ¢ ¢ ¢ im
rows of A, and the n 1 matrices
£
2 3
a1j

6 a2j 7
6 7
4 . 5
.

anj

are called columns of A. An n m matrix thus consists of n rows and m columns; a denotes the
£ ij
element, or entry, of A in the ith row and j th column. A matrix consisting of just one row is called
a row vector, whereas a matrix of just one column is called a column vector. The elements of a
vector are frequently ponents of the vector. When the size of the matrix is clear from the
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