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Unformatted text preview: 3. The exponential of a square matrix A can be deﬁned by the power series: e A = ∞ X n =0 1 n ! A n (1) = I + A + 1 2! A 2 + 1 3! A 3 + ... (2) where I is the unit (identity) matrix. (a) Use a Do loop to print out the results of the sum in Eq. (2) term by term up to n = 10 for the matrix: A = ˆ-1-1 1-1 ! . (3) Hint: Use the Mathematica function MatrixPower[A,n] to evaluate A n . Note that writing A^n does not in general give the same result as MatrixPower[A,n] . (b) Use the function MatrixExp to obtain a symbolic expression for exp( A ). Evaluate this expression numerically and compare it to what you obtained using the Taylor series expression for n = 10. Within Mathematica , does MatrixExp[A] give the same result as Exp[A] ? If not, how do the two diﬀer? (c) Use the function MatrixExp to obtain a symbolic expression for e B and e C where B = ˆ 0 1 1 0 ! (4) and C = ˆ-x x ! . (5) Ponder your results....
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This note was uploaded on 12/29/2011 for the course ENGR 5a taught by Professor Brewer during the Fall '09 term at UCSB.
- Fall '09
- Chemical Engineering