Linear_algebra - Wikiparency

# Linear algebra  ## Microsims — p5.js ### Linear algebra (p5.js) · `A x = b` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/WK2jkPa5k" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Linear algebra — p5.js microsim"></iframe> </div> *The mathematics of vectors and matrices — the framework in which nearly all DSP computation lives.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/WK2jkPa5k) · movement *IX · Foundations & the rest of the toolbox* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Calculus]] *(in tree)* - [[Complex_analysis]] *(in tree)* - [[Control_theory]] *(in tree)* - [[Fourier_analysis]] *(in tree)* - [[Functional_analysis]] *(in tree)* - [[Graph_theory]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Links (Wikipedia order)  `3Blue1Brown` · `A_Treatise_on_Electricity_and_Magnetism` · `Abelian_group` · `Abstract_algebra` · `Additive_inverse` · `Adjugate_matrix` · `Affine_geometry` · `Affine_group` · `Affine_space` · `Affine_transformation` · `Algebra` · `Algebra_over_a_field` · `Algebraic_geometry` · `Algebraic_number_theory` · `Algebraic_topology` · [[Algorithm]] · `American_Mathematical_Society` · `Analytic_geometry` · `Analytic_number_theory` · `Applied_mathematics` · `Arithmetic` · `Arithmetic_geometry` · `Arthur_Cayley` · `Atmosphere` · `Augmented_matrix` · `Axiom` · `Banach_space` · `Basic_Linear_Algebra_Subprograms` · `Basis_(linear_algebra)` · `Benjamin_Peirce` · `Bijection` · `Bilinear_form` · `Binary_operation` · `Bivector` · `Block_matrix` · `Bra–ket_notation` · `Cache_(computing)` · [[Calculus]] · `Canonical_map` · `Cardinality` · [[Cartesian_coordinate_system]] · `Category_theory` · `Cauchy–Binet_formula` · `Cauchy–Schwarz_inequality` · `Cayley–Hamilton_theorem` · `Change_of_basis` · `Characteristic_polynomial` · `Charles_F._Van_Loan` · `Charles_Royal_Johnson` · `Charles_Sanders_Peirce` · `Cholesky_decomposition` · `Circulant_matrix` · `Clifford_algebra` · `Closed-form_expression` · `Cokernel` · `Combinatorics` · `Commutative_algebra` · `Commutative_ring` · `Comparison_of_linear_algebra_libraries` · `Complete_metric_space` · [[Complex_analysis]] · `Complex_conjugate` · `Complex_geometry` · `Complex_number` · `Complex_plane` · [[Complex_system]] · `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]] · `Convex_geometry` · `Coordinate_vector` · `Coral_Gables,_Florida` · `Cramer's_rule` · `Cyclic_subspace` · `Dan_Margalit_(mathematician)` · `Data_structure` · `David_Tall` · `Determinant` · `Diagonal_matrix` · `Diagonalizable_matrix` · `Dianne_Hansford` · `Differential_(mathematics)` · [[Differential_equation]] · `Differential_geometry` · `Differential_topology` · `Dimension_(vector_space)` · `Dimension_theorem_for_vector_spaces` · `Diophantine_geometry` · `Discrete_geometry` · `Discrete_mathematics` · `Discretization` · `Dot_product` · `Dual_basis` · `Dual_space` · `Eigenvalues_and_eigenvectors` · `Electric_power_distribution` · [[Electric_power_transmission]] · `Elementary_algebra` · `Elementary_matrix` · `Emil_Artin` · `Encyclopedia_of_Mathematics` · `Endomorphism` · [[Engineering]] · [[Engineering_mathematics]] · `Equipollence_(geometry)` · `Euclidean_geometry` · `Euclidean_group` · `Euclidean_space` · `Examples_of_vector_spaces` · `Exterior_algebra` · `Felix_Gantmacher` · `Field_(mathematics)` · `Field_extension` · `Finite_field` · `Finite_geometry` · `Finitely_generated_module` · `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)` · `Future_of_mathematics` · `Gabriel_Cramer` · `Gainesville,_Florida` · `Gamas's_theorem` · [[Game_theory]] · `Gaussian_elimination` · `Gene_H._Golub` · `General_linear_group` · `General_topology` · `Geodesy` · `Geometric_Algebra_(book)` · `Geometric_algebra` · `Geometric_topology` · `Geometric_transformation` · [[Geometry]] · `Georgiy_Shilov` · `Gilbert_Strang` · `Glossary_of_linear_algebra` · `Glossary_of_mathematical_symbols` · `Gottfried_Wilhelm_Leibniz` · `Graduate_Texts_in_Mathematics` · `Gram–Schmidt_process` · [[Graph_theory]] · `Group_representation` · `Group_theory` · `Hankel_matrix` · `Harmonic_analysis` · `Harry_Dym` · `Haynsworth_inertia_additivity_formula` · [[Heat_transfer]] · `Henryk_Minc` · `Hermann_Grassmann` · `Hermitian_matrix` · `Hessenberg_matrix` · `Hessian_matrix` · `Higher-order_singular_value_decomposition` · `Hilbert_space` · `History_of_Lorentz_transformations` · `History_of_mathematics` · `Homography` · `Homological_algebra` · `Homotopy_theory` · `Householder_transformation` · `Hypercomplex_number` · `IBM` · `IEEE_Transactions_on_Computers` · `Ian_Stewart_(mathematician)` · `Identity_element` · `Identity_matrix` · `Igor_Shafarevich` · `Improper_rotation` · `Indefinite_orthogonal_group` · `Informal_mathematics` · `Information_geometry` · [[Information_theory]] · `Inner_product_space` · `Inverse_element` · `Invertible_matrix` · `Isometry` · `Isomorphism` · `Israel_Gelfand` · `James_Clerk_Maxwell` · `James_Demmel` · `James_Joseph_Sylvester` · `Jim_Hefferon` · `Johns_Hopkins_University_Press` · `Jordan_normal_form` · `Kernel_(linear_algebra)` · `LAPACK` · `LU_decomposition` · `Large_numbers` · `Least_squares` · `Leon_Mirsky` · `Limit_(mathematics)` · `Line_(geometry)` · `Linear_Algebra_(book)` · `Linear_combination` · `Linear_equation` · `Linear_equation_over_a_ring` · `Linear_form` · `Linear_function` · `Linear_independence` · `Linear_least_squares` · `Linear_map` · `Linear_programming` · `Linear_regression` · `Linear_span` · `Linear_subspace` · `Linear_system` · `List_of_films_about_mathematicians` · `Lists_of_mathematics_topics` · `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_linguistics` · `Mathematical_logic` · [[Mathematical_model]] · [[Mathematical_optimization]] · `Mathematical_physics` · `Mathematical_psychology` · `Mathematical_sociology` · `Mathematical_statistics` · `Mathematics` · `Mathematics_and_art` · `Mathematics_education` · `Matrix_(mathematics)` · `Matrix_addition` · `Matrix_congruence` · `Matrix_consimilarity` · `Matrix_decomposition` · `Matrix_equivalence` · `Matrix_multiplication` · `Matrix_similarity` · `Measure_(mathematics)` · `Mechanics` · `Minor_(linear_algebra)` · `Module_(mathematics)` · `Module_homomorphism` · `Monic_polynomial` · `Multi-core_processor` · `Multilinear_algebra` · `Multiplicative_inverse` · `Multivector` · `Möbius_transformation` · `Navier–Stokes_equations` · [[Nonlinear_system]] · `Norm_(mathematics)` · `Normal_matrix` · `Normed_vector_space` · `Null_vector` · `Nullity_theorem` · `Number` · `Number_theory` · `Numerical_analysis` · `Numerical_linear_algebra` · `Numerical_stability` · [[Operations_research]] · `Orientation_(geometry)` · `Orthogonal_basis` · `Orthogonal_complement` · `Orthogonal_group` · `Orthogonal_matrix` · [[Orthogonality]] · `Outer_product` · `Outline_of_linear_algebra` · `Overcompleteness` · `Parametrization_(atmospheric_modeling)` · `Parametrization_(geometry)` · `Parity_of_a_permutation` · [[Partial_differential_equation]] · `Paul_Halmos` · `Perron–Frobenius_theorem` · `Perspectivity` · `Pfaffian` · `Philosophy_of_mathematics` · `Poincaré_group` · `Pointwise` · `Polar_decomposition` · `Polynomial` · `Polynomial_ring` · `Principal_ideal_domain` · `Probability_theory` · `Processor_(computing)` · `Projection_(linear_algebra)` · `Projection_(mathematics)` · [[Projective_geometry]] · `Projective_linear_group` · `Projective_space` · `Pseudo-Euclidean_space` · `QR_decomposition` · `Quadratic_form` · `Quadric` · [[Quantum_mechanics]] · `Quaternion` · `Range_of_a_function` · `Rank_(linear_algebra)` · `Rank–nullity_theorem` · `Ray_Kunze` · `Real_analysis` · `Real_number` · `Recreational_mathematics` · `Reducing_subspace` · `Reflection_(mathematics)` · `Reinhold_Remmert` · `Renewable_energy` · `René_Descartes` · `ResearchGate` · `Rigid_body_dynamics` · `Ring_(mathematics)` · [[Robotics]] · `Rod_calculus` · `Roger_Horn` · `Rotation` · `Rotation_(mathematics)` · `Row_and_column_spaces` · `Row_equivalence` · `Scalar_multiplication` · `Schur_complement` · `Schur_decomposition` · [[Sequence]] · `Serge_Lang` · `Sergei_Treil` · `Sesquilinear_form` · `Set_(mathematics)` · [[Set_theory]] · `Shear_mapping` · `Sheldon_Axler` · `Shin_Takahashi` · `Singular_matrix` · `Singular_value_decomposition` · `Skew-symmetric_matrix` · `Smart_grid` · `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` · `Synthetic_geometry` · `System_of_linear_equations` · [[Systems_science]] · [[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` · `University_Press_of_Florida` · `University_of_Miami` · `University_of_Queensland` · `Vandermonde_matrix` · `Vector_(mathematics_and_physics)` · `Vector_space` · `Wave_function` · [[Weather_forecasting]] · `Weyr_canonical_form` · `William_Rowan_Hamilton` · `Woodbury_matrix_identity` · `Yitzhak_Katznelson` · `Zero_matrix` > Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg  !480 *Rendered from the live microsim (▶ motion).*  ## See it next [![Vector spaces|200](Vector_spaces_thumb.png)](Vector_spaces) *→ Vector spaces*  --- Back to Signal Processing Portal · the room · Semiotic gateway  ## What it is Linear algebra is the branch of mathematics concerned with vectors, vector spaces, linear maps between them, and systems of linear equations, typically represented by matrices. ## How it works / why it matters It is the working language of signal processing: signals are vectors, transforms and filters are matrices or linear operators, and operations like the DFT, convolution, and least-squares estimation are matrix computations. Concepts such as eigenvalues, orthogonal bases, and singular value decomposition explain filter behaviour, dimensionality reduction, and the stability and invertibility of linear systems. ## Signs & universals Instantiates: transformation signal system ## Related Vector spaces · [[Functional_analysis]] · [[Adjacency_matrix]] · Optimization · [[Convolution]] · Discrete Fourier transform  ## From the Real GENERATIVE library > Linear algebra is the branch of mathematics concerning linear equations such as: ([Wikipedia](https://en.wikipedia.org/wiki/Linear_algebra))   *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Linear_algebra) : [Wikitube](https://en.wikitube.io/wiki/Linear_algebra) ## Previous hub tags Tree parents: [[Control_theory]] · [[Game_theory]] · [[Graph_theory]] · [[Information_theory]] · [[Operations_research]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*