
A
Linear Algebra Review
Definition A.1 A matrix A is a rectangular array of numbers. The size of
A is denoted by m × n where m is the number of rows and n is the number
of columns of A. If m = n, then A is called a square matrix.
Example A.2
The following matrices
A =
1 4 −3
−12 9 2
, B =
2
−4
5
, C =
3 1 2
5 2 8
1 7 4
, D =
1 0 −5
have dimension 2 × 3, 3 ×1, 3 × 3, and 1 × 3, respectively. The
matrix C is a square matrix with m = n = 2.
Let A be a m ×n matrix. We denote a
ij
as the element of A that is in the
ith row and jth column. Then, the matrix A can be specified as A = [a
ij
] for
1 ≤ i ≤ m and 1 ≤ j ≤ n.
Definition A.3
A vector v of dimension k is a matrix ...