matrix inversion

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matrix inversion

A student calculates the matrix inversion on a chalkboard.

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.
matrix inversion

A student calculates the matrix inversion on a chalkboard.

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