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The 21 pages that link to Identity matrix, each with the reason it gives.

• EigenvalueRelated: Subtracting a scalar multiple of it forms the matrix used to test eigenvalues.

• Matrix multiplicationRelated: Multiplying by it leaves a compatible matrix unchanged.

• Characteristic polynomialRelated: It makes λI − A a matrix whose determinant defines the polynomial.

• Matrix exponentialRelated: It is the constant term in the power series and the exponential's value at zero.

• Invertible matrixRelated: An inverse is defined by multiplying to this matrix.

• LU decompositionRelated: It is the starting factor in elimination and the neutral element in matrix products.

• Orthogonal matrixRelated: Multiplying an orthogonal matrix by its transpose gives the identity.

• OneRelated: Its diagonal entries are one, preserving vectors under matrix multiplication.

• Cayley–Hamilton theoremRelated: It supplies the matrix counterpart of the scalar constant term in the characteristic polynomial.

• Kronecker deltaRelated: Its entries are precisely the Kronecker delta values.

• Cramer's ruleRelated: The inverse condition is defined by multiplication producing this matrix.

• Laplace expansionRelated: Its sparse rows and columns make determinant expansions immediate.

• Sherman–Morrison formulaRelated: Multiplying the proposed updated inverse by the updated matrix must yield this matrix.

• Woodbury matrix identityRelated: It appears in the reduced matrix whose inverse corrects the original inverse.