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The 17 pages that link to Matrix exponential, each with the reason it gives.

• EigenvalueRelated: Eigenvalues determine growth or decay rates in continuous-time linear dynamics.

• Jordan normal formRelated: Jordan blocks reduce its computation to exponentials multiplied by finite polynomials.

• 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.

• 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.

• Liouville's formulaRelated: For constant coefficients, the fundamental matrix is a matrix exponential whose determinant follows the formula.