Ps1soln - Solutions to Problem Set#1 EECE-595 Section II Spring 2003 Adaptive Filtering Date Assigned Date Due Problem 1.0 Let us first multiply

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Unformatted text preview: Solutions to Problem Set #1 EECE-595, Section II Spring 2003, Adaptive Filtering Date Assigned: 02/10/03 Date Due: 02/17/03 Problem # 1.0 Let us first multiply the matrix A + BCD on the left by suggested inverse: LHS = ( A- 1- A- 1 B ( C- 1 + DA- 1 B )- 1 DA- 1 )( A + BCD ) Multiplying the four different terms we obtain the result: LHS = I + A- 1 BCD- A- 1 B ( C- 1 + DA- 1 B )- 1 D- A- 1 B ( C- 1 + DA- 1 B )- 1 DA- 1 BCD . Factoring a A- 1 B ( C- 1 + DA- 1 B )- 1 common on the left and a CD common on the right we obtain: LHS = I + A- 1 B ( C- 1 + DA- 1 B )- 1 ( C- 1 + DA- 1 B- C- 1- DA- 1 B ) CD LHS = I . If on the other hand we multiply the matrix A + BCD on the right hand side we obtain: RHS = ( A + BCD )( A- 1- A- 1 B ( C- 1 + DA- 1 B )- 1 DA- 1 ) Again multiplying the four different terms out we obtain: RHS = I- B ( C- 1 + DA- 1 B )- 1 DA- 1- BCDA- 1 B ( C- 1 + DA- 1 B )- 1 DA- 1 + BCDA- 1 ....
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This note was uploaded on 12/02/2011 for the course AR 107 taught by Professor Gracegraham during the Fall '11 term at Montgomery College.

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Ps1soln - Solutions to Problem Set#1 EECE-595 Section II Spring 2003 Adaptive Filtering Date Assigned Date Due Problem 1.0 Let us first multiply

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