How deeply does Geometry for Programmers cover matrix inversion?

Defines inverse matrices and identity multiplication, but defers manual algorithms and detailed applications.

Matrix inversion

As explained in Geometry for Programmers

Matrix inversion is the operation of finding a matrix that multiplies with a given matrix to produce an identity matrix, when such a matrix exists.

Matrix inversion finds a matrix that multiplies with a given matrix to produce an identity matrix. Such an inverse may or may not exist. section 2.5.2

The operation is useful for undoing a geometrical transformation: multiplying by the inverse reverses the original matrix transformation. section 2.5.2

Keep these practical points in mind:

Treat the identity matrix as the result that leaves the represented transformation unchanged. section 2.5.2
Expect matrix orientation to matter, because transposition changes rows into columns and can affect how routines operate. section 2.5.2
Use SymPy when manual inversion is unnecessary; hand methods remain available for learning how inversion works. section 2.5.2

An inverse pair

Given a matrix and its inverse, either matrix can be multiplied by the other to obtain the identity matrix. Swapping the two matrices preserves the relationship. section 2.5.2

How Geometry for Programmers covers it

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Also explained in

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Hacking CryptographyMatrix inversion is the operation of finding a matrix that multiplies with a given invertible matrix to produce the identity matrix.

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Related concepts

cofactor transpositionalternative to · Cofactor transposition is the construction of a transposed cofactor matrix that represents a matrix inverse up to multiplication by the determinant.
diagonalizationcontrasts with · A matrix transformation technique that expresses a square matrix in a basis where it becomes diagonal, simplifying computations such as powers.
linear systemaddressed by · A linear system is a set of linear relationships among variables, commonly expressed as simultaneous equations or a linear transformation, for which superposition applies.
singular value decompositioncontrasts with · Singular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal or unitary matrices and a diagonal matrix of nonnegative singular values.
determinantcontrasts with · A determinant is a scalar computed from a square matrix that characterizes properties such as invertibility and signed volume scaling.
projective transformationuses · A projective transformation is a mapping of projective-space points represented by homogeneous linear coordinates that preserves incidence but may not preserve parallelism.

This explainer was generated by Manning's knowledge graph from the text of Geometry for Programmers. The section links point to the parts of the book it draws on.