TABLE OF CONTENTS A matrix is a rectangular array. The matrix
is called an m n matrix, meaning there are m rows and n columns. The vector
is an n 1 column vector. The vector
is a 1 m row vector. The dimension of a vector is the number of elements in the vector; e.g., the dimension of the vector x above is n. Matrices can be thought of as consisting of row vectors stacked vertically, or column vectors stacked horizontally.
The transpose of a matrix is the matrix obtained by switching the rows and columns. For the matrix A in Eq. (A.1), the transpose is an n m matrix
Matrices with the same dimensions can be added by adding their corresponding elements,
Multiplying a matrix by a scalar is the same as multiplying each element in the matrix by that scalar,
for any scalar k. Two matrices A and B can be multiplied in the order AB if the number of columns of A equals the number of rows of B . When this is true, the matrices A and B are said to be conformable or to have conformable dimensions. The product of an m n matrix A with an n P matrix B is an m P matrix C, computed as
In general, matrix multiplication is not commutative, so AB
