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!
The Matrix Exponential (with exercises) by D. Klain Version 2017.01.05 Corrections and comments are welcome. The Matrix Exponential For each n ncomplex matrix A, de ne the exponential of Ato be the matrix
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