Chapter 5, "Matrix Operations"

Equal Matrices

Two matrices are equal if

• Both matrices have equal dimensions.

• All corresponding entries are equal.

Adding Matrices

For two matrices of the same size, add the corresponding entries.

Subtracting Matrices

For two matrices of the same size, subtract the corresponding entries.

Scalar Multiplication

for any scalar value c and any size matrix A.

Multiplying Two 2x2 Matrices

Is the Product Defined?

For matrix multiplication AB, the number of columns in A must equal the number of rows in B.

Size of the Product

If AB is defined, the size of matrix AB is the number of rows in A by the number of columns in B.

Matrix Multiplication Is Not Commutative

AB BA

for any size matrices A and B.

Transpose for a 3x3 Matrix

Transpose

For any size matrix A, each entry a_mn moves to a_nm in A^T.