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Linear algebra

Definition

Linear algebra is the branch of mathematics concerning linear equations such as

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Van Loan Charles Royal Johnson Charles Sanders Peirce Cholesky decomposition Circulant matrix Classical treatment of tensors Clifford algebra Closed-form expression Cokernel Column matrix Combinatorics Commutative algebra Commutative ring Commutativity Comparison of linear algebra libraries Complete metric space Complex analysis Complex conjugate Complex geometry Complex number Complex plane Complex system Component-free treatment of tensors Composite function Computational complexity Computational complexity theory Computational fluid dynamics Computational geometry Computational mathematics Computer algebra Computer graphics Computer science Computer vision Control Data Corporation Control theory Coordinate change Coordinate vector Coordinates Coral Gables, Florida Cramer's rule Cray Research, Inc.Cyclic subspace Dan Margalit (mathematician)Data structure Definite bilinear form Determinant Diagonal matrix Diagonalizable matrix Dianne Hansford Differential (mathematics)Differential equation Differential equations Differential geometry Differential topology Dimension (vector space)Dimension theorem for vector spaces Diophantine geometry Discrete geometry Discrete mathematics Discretization Distributivity Dot product Double dual Dual basis Dual space Earth shape Eigenvalue Eigenvalue, eigenvector and eigenspace Eigenvalues and eigenvectors Electric power distribution Electric power transmission Element (mathematics)Elementary algebra Elementary matrix Elementary row operation Elementary row operations Emil Artin Encyclopedia of Mathematics Endomorphism Engineering Engineering mathematics Equipollence (geometry)Euclidean geometry Euclidean group Euclidean space European Mathematical Society Examples of vector spaces Exterior algebra Felix Gantmacher Field (mathematics)Field extension Field theory (physics)Finite field Finite geometry Finitely generated module First-order approximation Flat (geometry)Floating-point arithmetic Fluid dynamics Fluid mechanics Foundations of mathematics Fourier analysis Free module Frobenius normal form Function (mathematics)Function composition Function space Functional analysis Fundamental matrix (computer vision)Fundamental theorem of finitely generated abelian groups Future of mathematics Gabriel Cramer Gainesville, Florida Galilean group Gamas's theorem Game theory Gauss Gaussian elimination Gauss–Jordan elimination Gene H. Golub General linear group General topology Generating set Geodesy Geometric Algebra (book)Geometric algebra Geometric topology Geometric transformation Geometry Georgia Institute of Technology Georgiy Shilov Gilbert Strang Glossary of linear algebra Glossary of mathematical symbols Gottfried Wilhelm Leibniz Graduate Texts in Mathematics Gram–Schmidt Gram–Schmidt process Graph theory Graphics processing units Group representation Group theory Hamel basis Hamel dimension Hankel matrix Harmonic analysis Harry Dym Haynsworth inertia additivity formula Heat transfer Henryk Minc Hermann Grassmann Hermitian conjugate Hermitian matrix Hessenberg matrix Hessian matrix Higher-order singular value decomposition Hilbert space History of Lorentz transformations History of mathematics Homogeneous system of linear equations Homography Homological algebra Homotopy theory Houghton Mifflin Company Householder transformation Hypercomplex analysis Hypercomplex number IBM IEEE Transactions on Computers Identity element Identity matrix Igor Shafarevich Image (function)Improper rotation Indefinite orthogonal group Informal mathematics Information theory Inner product Inner product space Interscience Publishers Inverse element Inverse image Inverse matrix Invertible matrix Isometry Isomorphic Isomorphism Israel Gelfand JHU Press James Clerk Maxwell James Demmel James Joseph Sylvester Jim Hefferon John Wiley & Sons Johns Hopkins University Press Jordan normal form Kernel (linear algebra)Kernel (linear operator)Knot theory LAPACK LU decomposition Large numbers Least squares Leon Mirsky Limit (mathematics)Line (geometry)Linear Linear Algebra (book)Linear combination Linear equation Linear equation over a ring Linear form Linear function Linear functional Linear independence Linear least squares Linear map Linear mapping Linear programming Linear regression Linear span Linear subspace Linear system Linearly independent List of films about mathematicians List of mathematicians List of matrices Lists of mathematics topics Lloyd N. Trefethen Lorentz transformation Lp space Main diagonal Manifold Map (mathematics)Marie A. Vitulli Marvin Marcus MathWorld Mathematical analysis Mathematical and theoretical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical geology Mathematical linguistics Mathematical logic Mathematical model Mathematical optimization Mathematical physics Mathematical psychology Mathematical sociology Mathematical statistics Mathematicians Mathematics Mathematics and art Mathematics education Matrix (mathematics)Matrix addition Matrix congruence Matrix consimilarity Matrix decomposition Matrix equivalence Matrix inverse Matrix inversion Matrix multiplication Matrix similarity Measure (mathematics)Mechanics Metric (mathematics)Minor (linear algebra)Module (mathematics)Module homomorphism Monic polynomial Moore–Penrose pseudoinverse Multi-core processor Multilinear algebra Multiplicative identity Multiplicative inverse Multivariate function Multivector Möbius transformation Navier–Stokes equations Non-linear Nonlinear system Nonlinear systems Norm (mathematics)Normal matrix Normed vector space Null space Null vector Nullity theorem Number Number theory Numerical analysis Numerical linear algebra Numerical stability Operations research Order theory Orientation (geometry)Orthogonal basis Orthogonal complement Orthogonal group Orthogonal matrix Orthogonal projection Orthogonality Outer product Outline of linear algebra Overcompleteness Parametrization (atmospheric modeling)Parametrization (geometry)Parity of a permutation Partial differential equation Paul Halmos Peano Perron–Frobenius theorem Perspectivity Pfaffian Philosophy of mathematics Plane (geometry)Poincaré group Pointwise Polar decomposition Polynomial Polynomial ring Positive-definite matrix Power systems Preimage Prentice-Hall Principal ideal domain Prindle, Weber and Schmidt Probability theory Processor (computing)Projection (linear algebra)Projection (mathematics)Projective geometry Projective linear group Projective space Projective transformation Pseudo-Euclidean space QR decomposition Quadratic form Quadric Quantum mechanics Quaternion Range of a function Rank (linear algebra)Rank of a matrix Rank–nullity theorem Ray Kunze Real analysis Real number Recreational mathematics Reduced row echelon form Reducing subspace Reflection (mathematics)Reinhold Remmert Renewable energy René Descartes ResearchGate Rigid body dynamics Rigid motion Ring (mathematics)Robotics Rod calculus Roger Horn Root of a function Rotation Rotation (mathematics)Row and column spaces Row equivalence Scalar multiplication Schur complement Schur decomposition Scientific computation Sequence Sequence (mathematics)Serge Lang Sergei Treil Sesquilinear form Set (mathematics)Set theory Shear mapping Sheldon Axler Shin Takahashi Similar (linear algebra)Singular matrix Singular value decomposition Skew-symmetric matrix Smart grid Space of functions Spanning set Sparse matrix Spectral theorem Spectrum of a matrix Springer Publishing Springer Science+Business Media Square-free polynomial Square matrix Squeeze mapping Statistics Steven Roman Stochastic matrix Strassen algorithm Subset Symmetric algebra Symmetric group Symmetric matrix Symplectic structure Synthetic geometry System of linear equations Systems of linear equations Systems science Telegraph Tensor Tensor algebra Tensor product The Nine Chapters on the Mathematical Art Theory of computation Thermal energy Three-dimensional space Timeline of mathematics Toeplitz matrix Topological space Topological vector space Topology Trace (linear algebra)Transformation matrix Translation (geometry)Transpose Transpose of a linear map Triangular matrix Tridiagonal matrix Tuple Type theory Undergraduate Texts in Mathematics Unitary matrix Universal algebra University Press of Florida University of Miami University of Queensland Vandermonde matrix Vector (mathematics and physics)Vector addition Vector space Vector spaces Wave function Weather forecasting Weyr canonical form William Rowan Hamilton Woodbury matrix identity Yerevan, Armenia Yitzhak Katznelson Zero matrix Zero vector

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