Page 20 - A Course in Linear Algebra with Applications

4 Chapter One: Matrix Algebra

(ii) An m x 1 matrix, or m-column vector, B has just one
column

b 2i
B =

\bml/

(iii) A matrix with the same number of rows and columns is
said to be square.
(iv) A zero matrix is a matrix all of whose entries are zero.
The zero m x n matrix is denoted by

or simply 0.
0m n
Sometimes 0 nn is written 0 n . For example, O23 is the matrix

0 0 0
0 0 0

(v) The identity nxn matrix has l's on the principal diagonal,
that is, from top left to bottom right, and zeros elsewhere; thus
it has the form
(\ 0 ••• 1 ^
0 1 ••• 0

\ 0 0 ••• 1 /

This matrix is written

or simply I.
I n
The identity matrix plays the role of the number 1 in matrix
multiplication.

(vi) A square matrix is called upper triangular if it has only
zero entries below the principal diagonal. Similarly a matrix