KnowraMatrix exponentialLinked fromLinked fromThe 17 pages that link to Matrix exponential, each with the reason it gives.All 17Broader topic 2Related 13Compared with 2EigenvalueRelated: Eigenvalues determine growth or decay rates in continuous-time linear dynamics.Complex exponentialBroader topic: It extends the same series definition to matrices, where exponentials can encode rotations and evolution.Jordan normal formRelated: Jordan blocks reduce its computation to exponentials multiplied by finite polynomials.Exponential mapCompared with: It is a related algebraic construction and often realizes the Lie group exponential for matrix groups.Linear differential equationRelated: It expresses solutions of linear systems of ordinary differential equations.Square matrixRelated: It turns a square matrix into an operator for continuous-time linear dynamics.Cayley–Hamilton theoremRelated: Power reduction can simplify computations of the exponential for a fixed finite-dimensional matrix.Floquet theoryRelated: Floquet normal form reduces periodic evolution to a constant matrix exponential.Diagonal matrixRelated: For a diagonal matrix, the exponential applies the scalar exponential to each diagonal entry.Jordan decompositionRelated: Commuting parts let the exponential factor into a semisimple contribution and a nilpotent polynomial factor.Matrix theoryRelated: It converts a matrix into the evolution operator for linear differential systems.Baker–Campbell–Hausdorff formulaCompared with: Directly multiplying exponentials avoids expanding their logarithm into commutators.Eigenvalues and eigenvectorsRelated: Eigenvalues make continuous-time linear evolution and matrix exponentials easier to analyze.Jordan–Chevalley decompositionRelated: Exponentiating commuting components separates exponential and unipotent behavior.Crank–Nicolson methodRelated: It provides the exact diffusion evolution against which time-stepping error can be assessed.Golden–Thompson inequalityBroader topic: Exponentials of A, B, and their sum are the quantities compared.Liouville's formulaRelated: For constant coefficients, the fundamental matrix is a matrix exponential whose determinant follows the formula.
KnowraMatrix exponentialLinked fromLinked fromThe 17 pages that link to Matrix exponential, each with the reason it gives.All 17Broader topic 2Related 13Compared with 2EigenvalueRelated: Eigenvalues determine growth or decay rates in continuous-time linear dynamics.Complex exponentialBroader topic: It extends the same series definition to matrices, where exponentials can encode rotations and evolution.Jordan normal formRelated: Jordan blocks reduce its computation to exponentials multiplied by finite polynomials.Exponential mapCompared with: It is a related algebraic construction and often realizes the Lie group exponential for matrix groups.Linear differential equationRelated: It expresses solutions of linear systems of ordinary differential equations.Square matrixRelated: It turns a square matrix into an operator for continuous-time linear dynamics.Cayley–Hamilton theoremRelated: Power reduction can simplify computations of the exponential for a fixed finite-dimensional matrix.Floquet theoryRelated: Floquet normal form reduces periodic evolution to a constant matrix exponential.Diagonal matrixRelated: For a diagonal matrix, the exponential applies the scalar exponential to each diagonal entry.Jordan decompositionRelated: Commuting parts let the exponential factor into a semisimple contribution and a nilpotent polynomial factor.Matrix theoryRelated: It converts a matrix into the evolution operator for linear differential systems.Baker–Campbell–Hausdorff formulaCompared with: Directly multiplying exponentials avoids expanding their logarithm into commutators.Eigenvalues and eigenvectorsRelated: Eigenvalues make continuous-time linear evolution and matrix exponentials easier to analyze.Jordan–Chevalley decompositionRelated: Exponentiating commuting components separates exponential and unipotent behavior.Crank–Nicolson methodRelated: It provides the exact diffusion evolution against which time-stepping error can be assessed.Golden–Thompson inequalityBroader topic: Exponentials of A, B, and their sum are the quantities compared.Liouville's formulaRelated: For constant coefficients, the fundamental matrix is a matrix exponential whose determinant follows the formula.