Last update:  Tue Nov 28 14:00:48 MST 2006
Office Hours: Tuesday, 13:30-16:30
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             Math. 464/514, Fall'06 - Homework Assignments
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 Assignments based on G. Strang, LINEAR ALGEBRA AND ITS APPLICATIONS, 
                      4th edition, ISBN 0-03-010567-6
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 1( 8/22) Sec. 1.2-1.4 Geometry and Gaussian elimination
 2( 8/24) Sec. 1.5 Elementary triangular factors
    Set 1 (due 8/31): p.9, 1.2(1,3,8,9), p.15, 1.3(11, 24, 30), p.26, 1.4(4,24)
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 3( 8/29) Sec. 1.6 Inverses
 4( 8/31) Sec. 2.1 Vector Spaces
          Sec. 2.2 mXn systems
    Set 2 (due 9/ 7):  p.39, 1.5(4,9,11,13,18),
                       p.52, 1.6(10,11),
                       P.65, 1.R(4,5,12,13,18)
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 5( 9/ 5) Sec. 2.3 Linear Independence, Basis, Dimension
 6( 9/ 7) Sec. 2.4 Fundamental subspaces
    Set 3 (due 9/14): p.73, 2.1(2,7,8)
                      p.85, 2.2(4,5,7,8)
                      p.98, 2.3(2,6,8,10)
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 7( 9/12) Sec. 2.4 Fundamental subspaces
 8( 9/14) Sec. 2.4 continued
    Set 4 (due 9/21): p. 110, 2.4(1,3,5,6, 14, 16,17, 18, 27, 36)
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 9( 9/19) Sec. 2.5 Network and Graph Theory
10( 9/21) Sec. 2.6 Linear Transformations
    Set 5 (due 9/28): p. 124, 2.5(4,5,6,9,11,16,17,18,21)
                      p. 133, 2.6(6,7,18,47) 
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11( 9/26) Sec. 3.1 Orthogonal subspaces
          Sec. 3.2 Inner products
12( 9/28) Class cancelled
    Set 6 (due 10/5): p. 148, 3.1(7,9,12,16)
                      p. 157, 3.2(8,11)
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13(10/ 3) Sec. 3.3 Projection and Least Squares
14(10/ 5) Sec. 3.4 Orthogonalization and the Gram-Schmidt process
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15(10/10) Orthogonal Projections
    Set 7 (due 10/17) p. 170, 3.3(3*,6,11,12,15,18*,19,20*,24,25*,26*)
                      p. 185, 3.4(2*,4*,5,6,9,13,15,18,25)
           (problems marked by * are for practise; do not turn in!)
**(10/12-13)  Fall Break
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16(10/17) Ch.4.1-3: Some results on determinants.
    Set 8 (due 10/26) p. 206, 4.2(1,4,12,13,19,21,29,30)
                      p. 215, 4.3(3,6,34)
17(10/19) MIDTERM EXAM (Chapters 1-3)         
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18(10/24) Sec. 4.4: More on determinants
19(10/26) Sec. 5.1 Eigenvalues and Eigenvectors
          Sec. 5.2 Diagonal forms
          Sec. 5.4 Differential equations and exp(At)
    Set 9 (due 11/2) p. 226, 4.4(5) + 2 problems on p.6 of "Geometry" notes
                     p. 240, 5.1(5)
                     p. 250, 5.2(4,6,8,13)
                     p. 275, 5.4(1,4,5)
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20(10/31) Sec. 5.3 Difference equations and A^k
21(11/ 2) Sec. 5.5 Complex Matrices
    Set 10 (due 11/9) p. 262, 5.3(4,8,16,19)
                      p. 288, 5.5(7,8,11,19)
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22(11/ 7) Complex matrices
23(11/ 9) Sec. 5.6 Similarity
    Set 11 (due 11/21) p. 302, 5.6(4,7,13,24,28,29)
                       p. 307 review 5.(8,11,20)
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24(11/14) Generalized eigenspaces and the Jordan canonical form.
25(11/16) Sec. 6.1 Extrema and Quadratic Forms,  
          Sec. 6.2 Positive Definite Matrices
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26(11/21) Sec. 6.2 cont.: Symmetric Matrices and the Law of Inertia
    Set 12 (due 11/30) p.302, 5.6(39--hint: see prob.4, Appendix B), 
                       p.427, App.B (1)
                       p.316, 6.1(4,7,17)
                       p.326, 6.2(7,9,11,14,18,19,27,28) 
**(11/23-24) Thanksgiving Break
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27(11/28) Sec. 6.2 cont.: Symmetric Matrices and the Law of Inertia
          Locating eigenvalues
28(11/30) Sec. 6.3 The Singular Value Decomposition:
          Pseudoinverses and other applications of the SVD
          The computation of eigenvalues
      Set 13(due 12/7) p.326, 6.2(31,33,35,41) 
                       p.337, 6.3(2,5,8,15,18,23)
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29(12/ 5)  Pseudoinverses
30(12/ 7)  The optimal superposition problem (Procrustean transformations)
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----------- Final Examination (Thursday 12/14,  7:30-9:30 in Hum428)
                 (Open book)
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