Invertible matrix

Definition

In linear algebra, an invertible matrix is a square matrix that has an inverse. In other words, if a matrix is invertible, it can be multiplied by its inverse matrix to yield the identity matrix. Invertible matrices are the same size as their inverse.

Related concepts

(0,1)-matrix 3D graphics 3D simulations Addition Adjacency matrix Adjugate matrix Affine coordinate system Affine geometry Affine group Affine space Affine transformation Aiken Computation Laboratory Algebraic structure Almost all Alternant matrix Alternating sign matrix Anti-diagonal matrix Antihermitian matrix Arbitrary-precision arithmetic Arrowhead matrix Association for Computing Machinery Associativity Augmented matrix Band matrix Basic Linear Algebra Subprograms Basis (linear algebra)Basis of a vector space Basis transformation matrix Bell polynomials Biadjacency matrix Bidiagonal matrix Big O notation Binomial inverse theorem Bisymmetric matrix Bivector Block-diagonal matrix Block matrix Block tridiagonal matrix Boolean matrix Bézout matrix Cabibbo–Kobayashi–Maskawa matrix Cambridge University Press Cartan matrix Cartesian coordinate system Category of vector spaces Cauchy matrix Cauchy–Binet formula Cayley–Hamilton theorem Centering matrix Centrosymmetric matrix Change of basis Characteristic polynomial Charles E. Leiserson Cholesky decomposition Circulant matrix Classical treatment of tensors Clifford Stein Clifford algebra Closed set Cofactor matrix Commutation matrix Commutative ring Companion matrix Comparison of linear algebra libraries Complex Hadamard matrix Complex number Component-free treatment of tensors Computational complexity of matrix multiplication Computationally efficient Computer graphics Condition number Conference matrix Confusion matrix Conjugate transpose Continuous function Convergent matrix Copositive matrix Correlation matrix Covariance matrix Coxeter matrix Cramer's rule Cross product Cyclic subspace DFT matrix Defective matrix Definite matrix Degree matrix Dense set Density matrix Derivative of matrix Design matrix Determinant Diagonal matrix Diagonalizable matrix Diagonally dominant matrix Dimension theorem for vector spaces Diophantine equation Distance matrix Divide and conquer algorithm Dot product Doubly stochastic matrix Dual space Duplication and elimination matrices Edmonds matrix Eigendecomposition of a matrix Eigenvalue Eigenvalue, eigenvector and eigenspace Eigenvalues and eigenvectors Eigenvector Einstein summation Electronics Letters Elementary matrix Elementary row operations Encyclopedia of Mathematics Equivalent matrix Euclidean distance matrix Euclidean group Euclidean space European Mathematical Society Examples of vector spaces Exchange matrix Exterior algebra Family (set theory)Field (mathematics)Fisher information matrix Flat (geometry)Floating-point arithmetic Frequency band Frobenius matrix Fundamental matrix (computer vision)Fundamental matrix (linear differential equation)Fuzzy associative matrix Galilean group Gamas's theorem Gamma matrices Gaussian elimination Gauss–Jordan elimination Gell-Mann matrices General linear group Generalized inverse Generalized permutation matrix Generator matrix Geometric algebra Geometric sum Gilbert Strang Glossary of linear algebra Google Books Graduate Texts in Mathematics Gram matrix Gram–Schmidt process Grant Sanderson Graph theory Group (mathematics)Hadamard matrix Hamel basis Hamel dimension Hamiltonian matrix Hankel matrix Haynsworth inertia additivity formula Hermitian matrix Hessenberg matrix Hessian matrix Higher-order singular value decomposition Hilbert matrix Hollow matrix Homotopy Householder transformation Hurwitz-stable matrix Idempotent matrix Identity matrix If and only if Improper rotation Incidence matrix Indefinite orthogonal group Injective Inner product space Integer Integer matrix Introduction to Algorithms Inverse element Inverse of a matrix Involutory matrix Irregular matrix Jabotinsky matrix Jacobian matrix and determinant John Reif Jordan normal form Kernel (linear algebra)Kronecker delta LU decomposition Laplacian matrix Least squares Lebesgue measure Lehmer matrix Linear algebra Linear combination Linear equation Linear functional Linear independence Linear least squares Linear map Linear span Linear subspace List of matrices Logical matrix Lower triangular MIMO MIT OpenCourseWare Main diagonal Matrix (mathematics)Matrix addition Matrix congruence Matrix consimilarity Matrix decomposition Matrix equivalence Matrix exponential Matrix inversion Matrix multiplication Matrix multiplication algorithm Matrix of cofactors Matrix of ones Matrix product Matrix representation of conic sections Matrix similarity Matrix square root Matrix unit Measure theory Metzler matrix Minor (linear algebra)Moment matrix Moore matrix Moore–Penrose inverse Moore–Penrose pseudoinverse Multilinear algebra Multiplication Multiplicative inverse Multivector Necessary and sufficient condition Neumann series Newton's method Nilpotent matrix Noncommutative ring Nonnegative matrix Normal matrix Normed vector space Nowhere dense Null set Null space Null vector Nullity theorem Numerical analysis Numerical linear algebra Numerical stability Open set Orientation (geometry)Orthogonal Orthogonal complement Orthogonal group Orthogonal matrix Orthogonal projection Orthogonality Orthonormal Orthonormal basis Outer product Outline of linear algebra Overcompleteness Overlap matrix P-adic Parallelepiped Partial inverse of a matrix Pascal matrix Pauli matrices Payoff matrix Pentadiagonal matrix Perfect matrix Permutation matrix Perron–Frobenius theorem Persymmetric matrix Pfaffian Pick matrix Pivot position Poincaré group Polar decomposition Polynomial Polynomial matrix Positive-definite matrix Positive definite matrix Precision (statistics)Preconditioner Product rule Projection (linear algebra)Projection matrix Projective geometry Projective linear group Projective space Projective transformation Pseudo-Euclidean space Pseudoinverse QR decomposition Quadric Quaternionic matrix Ran Raz Random matrix Rank (linear algebra)Rank–nullity theorem Rational number Ray casting Real number Reciprocal (mathematics)Reciprocal basis Recursion Redheffer matrix Reducing subspace Ring (mathematics)Ron Rivest Rotation matrix Round-off error Routh–Hurwitz matrix Row and column spaces Row echelon form Row equivalence Rule of Sarrus Rybicki Press algorithm S-matrix Scalar (mathematics)Schur complement Schur decomposition Seidel adjacency matrix Seifert matrix Shear mapping Shear matrix Sheldon Axler Shift matrix Signature matrix Similarity matrix Singular matrix Singular value decomposition Skew-Hermitian matrix Skew-symmetric matrix Skyline matrix Sparse matrix Spectral theorem Spectrum of a matrix Springer Publishing Square matrix Squeeze mapping State-transition matrix Statistics Steven Roman Stieltjes matrix Stochastic matrix Strassen algorithm Subset Substitution matrix Surjective Sylvester matrix Symmetric algebra Symmetric matrix Symplectic matrix Symplectic structure System of linear equations Tensor Tensor algebra Thomas H. Cormen Toeplitz matrix Topological space Topological vector space Totally positive matrix Totally unimodular matrix Trace (linear algebra)Transformation matrix Transpose Triangular matrix Tridiagonal matrix Triple product Tutte matrix Undergraduate Texts in Mathematics Unimodular matrix Unipotent Unit (ring theory)Unitary matrix Vandermonde matrix Vector space Victor Pan Walsh matrix Weighing matrix Weinstein–Aronszajn identity Weyr canonical form Wireless communications Woodbury matrix identity Wronskian YouTube Z-matrix (chemistry)Z-matrix (mathematics)Zero matrix

23 concepts already in your glossary