Adjugate matrix

Definition

In linear algebra, the adjugate or classical adjoint adj(A) of a square matrix A is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that normally refers to a different concept, the adjoint operator which for a real matrix is the transpose.

Related concepts

Adjacency matrix Alston Scott Householder Alternant matrix Alternating sign matrix Anti-diagonal matrix Arrowhead matrix Augmented matrix Band matrix Basis (linear algebra)Bell polynomials Biadjacency matrix Bidiagonal matrix Bisymmetric matrix Block-diagonal matrix Block matrix Block tridiagonal matrix Boolean matrix Bézout matrix Cabibbo–Kobayashi–Maskawa matrix Canonical basis Cartan matrix Cauchy matrix Cauchy–Binet formula Cayley–Hamilton theorem Centering matrix Centrosymmetric matrix Characteristic polynomial Circulant matrix Cofactor (linear algebra)Cofactor matrix Column vector Commutation matrix Commutative ring Commuting matrices Companion matrix Complement (set theory)Complex Hadamard matrix Complex conjugation Complex number Compound matrix Conference matrix Confusion matrix Conjugate transpose Continuous function Continuously differentiable Convergent matrix Copositive matrix Corollary Correlation matrix Covariance matrix Coxeter matrix Cramer's rule DFT matrix Defective matrix Definite matrix Degree matrix Degree of a polynomial Density matrix Derivative Design matrix Determinant Diagonal matrix Diagonalizable matrix Diagonally dominant matrix Dimension (vector space)Diophantine equation Distance matrix Divided difference Doubly stochastic matrix Duplication and elimination matrices Edmonds matrix Eigenvalues and eigenvectors Elementary matrix Equivalent matrix Euclidean distance matrix Exchange matrix Exterior algebra Exterior product Faddeev–LeVerrier algorithm Felix Gantmacher Field (mathematics)Fisher information matrix Frobenius matrix Fundamental matrix (computer vision)Fundamental matrix (linear differential equation)Fuzzy associative matrix Gamma matrices Gell-Mann matrices Generalized permutation matrix Generator matrix Gilbert Strang Gram matrix Graph theory Hadamard matrix Hamiltonian matrix Hankel matrix Hermitian adjoint Hermitian matrix Hessenberg matrix Hessian matrix Hilbert matrix Hodge star operator Hollow matrix Householder transformation Hurwitz-stable matrix Idempotent matrix Identity matrix If and only if Incidence matrix Inner product Integer Integer matrix Inverse matrix Inverse of a matrix Invertible matrix Involutory matrix Irregular matrix Isomorphic Iterated function Jabotinsky matrix Jacobi's formula Jacobian matrix and determinant Jordan normal form Laplace expansion Laplacian matrix Lehmer matrix Linear algebra Linear independence Linear system of equations Linear transformation List of matrices Logical matrix Lower triangular matrix Mathematical proof Matrix (mathematics)Matrix congruence Matrix exponential Matrix of ones Matrix product Matrix representation of conic sections Matrix unit Metzler matrix Minor (linear algebra)Modular arithmetic Moment matrix Moore matrix Nilpotent matrix Nonnegative matrix Normal matrix Nullspace Orthogonal matrix Overlap matrix Pascal matrix Pauli matrices Payoff matrix Pentadiagonal matrix Perfect matrix Perfect pairing Permutation matrix Persymmetric matrix Pick matrix Polynomial Polynomial matrix Positive-definite matrix Precision (statistics)Projection (linear algebra)Projection matrix Pseudoinverse Pullback Quaternionic matrix Random matrix Rank (linear algebra)Real number Redheffer matrix Resolvent formalism Root of a polynomial Rotation matrix Routh–Hurwitz matrix Row echelon form S-matrix Seidel adjacency matrix Seifert matrix Shear matrix Shift matrix Signature matrix Similarity matrix Singular matrix Skew-Hermitian matrix Skew-symmetric matrix Skyline matrix Smooth function Sparse matrix Square matrix State-transition matrix Statistics Stieltjes matrix Stochastic matrix Submatrix Subset Substitution matrix Sylvester matrix Symmetric matrix Symmetric polynomial Symplectic matrix Toeplitz matrix Total derivative Totally positive matrix Totally unimodular matrix Trace (linear algebra)Trace diagram Transformation matrix Transpose Triangular matrix Tridiagonal matrix Tutte matrix Unimodular matrix Unipotent Unit (ring theory)Unital algebra Unitary matrix Upper triangular matrix Vandermonde matrix Vector space Walsh matrix Weighing matrix Wolfram Alpha Wronskian Z-matrix (chemistry)Z-matrix (mathematics)Zero matrix

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