Definition

1. Noun:
   • A mathematical operation: "Matrix inversion" is the process of finding the inverse of a given square matrix. The inverse of a matrix is another matrix that, when multiplied by the original matrix, yields the identity matrix (a unit matrix).

Usage

• "Matrix inversion" is a specific, singular term used in linear algebra. It refers to the computational or theoretical process itself.
• It is typically used in academic, scientific, and engineering contexts.
• Example:

Examples

• Noun:
  • The algorithm's efficiency depends on the speed of matrix inversion.
  • Performing matrix inversion on a large, dense matrix can be computationally expensive.
  • Understanding matrix inversion is fundamental to linear algebra.

Advanced Usage

• "to perform a matrix inversion": to carry out the operation of finding an inverse matrix.
  • The software package can perform a matrix inversion on matrices up to 1000x1000.
• "the problem of matrix inversion": referring to the computational challenges or theoretical aspects of the operation.
  • The lecture focused on the numerical stability of the matrix inversion problem.

Variants and Related Words

• Inverse matrix (n): The result of the matrix inversion operation.
  • After the matrix inversion, we obtained the inverse matrix.
• Invertible matrix (n): A matrix for which an inverse exists and matrix inversion is possible.
  • Only an invertible matrix is suitable for matrix inversion.
• Matrix inversion lemma (n): A specific mathematical identity useful in certain inversion calculations.

Synonyms

• Inversion of a matrix: A less common, but equivalent, phrasing.
• Finding the matrix inverse: A descriptive phrase for the same operation.

Related Concepts (Not Phrasal Verbs or Idioms)

• Identity matrix / Unit matrix: The matrix (with 1's on the diagonal and 0's elsewhere) that is the target product of a matrix and its inverse.
• Determinant: A scalar value that determines if a matrix is invertible; a zero determinant means matrix inversion is not possible.
• Linear equation solving: A primary application of matrix inversion.

Noun

1. determination of a matrix that when multiplied by the given matrix will yield a unit matrix