Transcription of The Matrix Exponential - UMass Lowell
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The Matrix Exponential - UMass Lowell
The Matrix Exponential (with exercises)by Dan and comments are Matrix ExponentialFor eachn ncomplex matrixA, define theexponentialofAto be the Matrix (1)eA= k=0 Akk!=I+A+12!A2+13!A3+ It is not difficult to show that this sum converges for all complex matricesAof any finitedimension. But we will not prove this a 1 1 Matrix [t], theneA= [et], by the Maclaurin series formula for the functiony=et. More generally, ifDis a diagonal Matrix having diagonal entriesd1,d2, .. ,dn,then we haveeD=I+D+12!D2+ = 10 001 ..00 0 1 + d10 00d2 ..00 0dn + d212!0 00d212! ..00 0d212! + = ed10 00ed2 ..00 0edn The situation is more complicated for matrices that are not diagonal.
The Matrix Exponential (with exercises) by Dan Klain Version 2018.09.28 Corrections and comments are welcome. The Matrix Exponential For each n n complex matrix A, define the exponential of A to be the matrix
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