Matrix Multiplication

Front

What is matrix multiplication?

Back

Matrix multiplication is a binary operation that produces a matrix from two matrices. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

If matrix A is of dimension (m x n) and matrix B is of dimension (n x p), what is the dimension of the product AB?

Back

The dimension of the product AB is (m x p).

Front

What is the condition for two matrices to be multiplied?

Back

Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Front

What is the result of multiplying a matrix by the identity matrix?

Back

Multiplying any matrix by the identity matrix of appropriate size results in the original matrix.

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero. It acts as the additive identity in matrix addition.

Front

How do you calculate the element in the i-th row and j-th column of the product of two matrices?

Back

To calculate the element in the i-th row and j-th column of the product, take the dot product of the i-th row of the first matrix and the j-th column of the second matrix.

Front

What is the associative property of matrix multiplication?

Back

The associative property states that for any matrices A, B, and C, (AB)C = A(BC), provided the products are defined.

Front

What is the distributive property of matrix multiplication?

Back

The distributive property states that A(B + C) = AB + AC for any matrices A, B, and C, provided the products are defined.

Front

Can matrix multiplication be commutative?

Back

In general, matrix multiplication is not commutative; that is, AB ≠ BA in most cases.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal, turning the row indices into column indices and vice versa.