Definition

1. Noun:
   • A specific mathematical operation: "Matrix multiplication" refers to the binary operation that produces a matrix from two matrices. It is a fundamental computation in linear algebra where the entries of the product matrix are calculated as the dot product of rows from the first matrix and columns from the second matrix.

Usage

• Matrix multiplication is not commutative; the order of the matrices matters (A × B ≠ B × A in general).
• It is defined only when the number of columns in the first matrix equals the number of rows in the second matrix.

Examples

• Noun:
  • The algorithm's efficiency depends heavily on the speed of matrix multiplication.
  • We performed matrix multiplication to transform the set of coordinates.
  • Understanding matrix multiplication is essential for computer graphics and machine learning.

Advanced Usage

• "Block matrix multiplication": A method for multiplying large matrices by partitioning them into smaller sub-matrices (blocks).
  • Using block matrix multiplication can improve computational performance by optimizing cache usage.

Variants and Related Words

• Matrix product (n): The result of performing matrix multiplication.
  • The matrix product of A and B is denoted as AB or A·B.
• Multiplicative (adj): Related to or involving multiplication.
  • The multiplicative identity for matrices is the identity matrix.
• Dot product (n): The scalar sum of products of corresponding entries, which is the core computation within matrix multiplication.
  • Each element in the product matrix is computed as a dot product.

Synonyms

• Matrix product formation
• Matrices multiplication

Related Phrases

• Chain of matrix multiplications: A sequence of multiplication operations.
  • The transformation is applied through a chain of matrix multiplications.
• Perform matrix multiplication: The act of carrying out the calculation.
  • The software library can perform matrix multiplication on GPU hardware.

Noun

1. the multiplication of matrices