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Glite Dictionary
identity matrix

identity matrix

6.7
A square table of numbers with ones on the diagonal and zeros elsewhere that acts like one when multiplying matrices
  • noun
  • /aɪˈdɛntɪti ˈmætrɪks/
  • Specialized
translation icon : matriz identidad
  • They're all the ways I can take the identity matrix and rearrange its rows.

They're all, as we said, the identity matrix brings us back to the two norm.

Examples

  • It's practically the identity matrix, but not quite.

  • But when he saw that new identity matrix, he found it incredibly compelling.

  • It's trying to be the identity matrix, right?

  • So this is B inverse times the identity matrix and then B.

  • I denotes an identity matrix of appropriate dimension.

    Academic text (2010)

  • The right hand side here is the identity matrix, which is the chronica delta MN.

  • But look, there's a really cute bit of algebra which happens because if I do, I the identity matrix minus my transition makes it just Q.

  • The identity matrix is essential in linear algebra because it acts as the multiplicative identity for matrix multiplication.

  • When multiplying any matrix by the identity matrix, the original matrix remains unchanged.

  • In this calculation, the identity matrix has ones along the diagonal and zeros in all other positions.

Synonyms

unit matrix
vsidentity matrix
  • Specialized
5.6

A square table of numbers with ones from the top left to the bottom right and zeros elsewhere

means the same but is the more common technical term

Surface Forms

identity matrix singular
identity matrices plural

Morphology

identity + matrix

A learner who knows 'identity' (something that preserves value) and 'matrix' (an arrangement of numbers) can infer that an 'identity matrix' is a matrix that acts as an identity—i.e., preserves vectors under multiplication. However, the precise structural definition (square form with ones on the diagonal and zeros elsewhere) is a technical mathematical convention not deducible from the everyday meanings of the words alone, so the relation is only partly predictable.

Etymology

The term identity matrix comes from the math idea of 'identity' — like the number 1, which 'leaves a number unchanged'. It is a square grid with ones on the diagonal and zeros elsewhere, and when you multiply a matrix by it the original matrix stays the same, so it 'does nothing' in multiplication.