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Elementary Linear Algebra 6e - Larson, Edwards, Falvo - Chapter 8 MATLAB - Complex Vector Spaces

Elementary Linear Algebra 6e - Larson, Edwards, Falvo - Chapter 8 MATLAB - Complex Vector Spaces

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CHAPTER 8 MATLAB EXERCISES 8–1 CHAPTER 8 MATLAB EXERCISES 1. MATLAB handles complex numbers and matrices in much the same way as real ones. The imaginary unit is a built-in constant. For instance, the complex number would be represented as in MATLAB. You can verify the result of Example 5, Section 8.2, by entering the matrix A , and then typing inv(A). Use MATLAB to perform the following matrix operations, given and (a) AB (b) (c) (d) (e) (f) 2. Use MATLAB to solve the system of linear equations (a) (b) 3. For a complex matrix A , the MATLAB command produces the complex conjugate transpose of A . Use this command to determine which of the following matrices are Hermitian and which are normal. (a) (b) (c) (d) 4. The MATLAB command will produce a diagonal matrix D containing the eigenval- ues of the complex matrix A , and a matrix P containing the corresponding eigenvectors. For instance,
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Unformatted text preview: 2 4 i 1 1 i 2 4 2 i 4 3 1 2 1 1 1 4 3 i 1 1 2 i 4 A p A , b 5 3 i 2 2 i 4 A 5 3 1 2 2 1 2 i i 1 1 i 2 i 2 1 4 , b 5 3 1 1 i 6 2 4 i 4 A 5 3 i 3 2 2 i 2 2 i 4 , A x 5 b . iAB 2 1 s 1 2 i d CC T | A 1 B | C T C A 2 1 3 iC C 5 3 i 2 2 i 2 1 3 i 4 . B 5 3 3 i 2 4 4 2 i 4 , A 5 3 1 2 1 i 2 2 i i 4 , A 5 f 2 2 i 2 5 1 2 p i ; 3 2 i 2 6 1 2 p i g 2 2 3 p i 2 2 3 i i 5 ! 2 1 8–2 CHAPTER 8 COMPLEX VECTOR SPACES and which is equivalent to the solution given in the text. Use this procedure to diagonalize the following matrices. (a) (b) (c) 3 1 1 2 i 1 1 i 1 1 i 2 i 1 2 i i 4 A 5 3 1 2 i i 2 4 A 5 3 1 i i 1 4 D 5 3 6.0000 1 0.0000 i 2 2.0000 1 0.0000 i 2 1.0000 2 0.0000 i 4 , P 5 3 0.7792 1 0.0000 i 0.3438 1 0.2063 i 0.0229 1 0.4813 i 2 0.4472 1 0.2236 i 0.1118 2 0.3354 i 0.1118 1 0.7826 i 2 0.2870 2 0.2460 i 2 0.2050 1 0.8199 i 0.2870 1 0.2460 i 4...
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