Math 510/590LH Fall 09

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Index

Homework 590LH see alternate assignments

510 Graded Homework (will be linked at least one week before due, are due at beginning of class unless stated otherwise)
For discussion (not graded):  All problems are for 510 unless marked otherwise
starred (*) probems are for 590LH also (prior to  Set 9 not marked)

Date
 Section
 Problems
Mon Aug 24
 1.2
 10, 13, 15
Wed Aug 26
 2.1
 2, 3, 7, 9, 11, 14
Fri Aug 28 2.4
 2, 3, 4, 9, 13, 15
Mon Aug 31 1.3
 5 -8, 11, 12, 14-16
Wed Sept 2
 more eigenvalues
 review lecture notes
Fri Sept 4
 2.5 1, 2, 3, 9, 11

2.6
 1, 2, 3
Wed Sept 9
 1.4
 2*, 4*, 5*, 6*
Fri Sept 11
Fill in details on Mathematica Schur demo snd use for other eigenvalue*
Mon Sept 14
 3.2
 4, 5
Wed Sept 16
 3.1
 2, 6, 8*, 9, 10*
Fri Sept 18
 3.1
 1

3.2
 7, 15*
Mon Sept 21
 3.2
 8*, 12, 14
Wed Sept 23
 3.2
 15*, 16
Fri Set 25
 3.3
 2*, 5, 7*, 8, 11, 12*, 14, 17, 18
Mon Sept 28
 diagonalization
Wed Sept 30
 3.4
Mon Oct 5
 3.4
 2*, 3*, 8*, 10*
Wed Oct 7
in CanForms2
Fri Oct 9
Example in CanForms2
Mon Oct 12
 4.1
 1*, 2*, 4*, 8*, 10,                          12(correction), 13, 17*
Wed Oct 14
 4.2 (not for 510, is in 590)
 2*,  3*, 5*,  6*, 7*
Fri Oct 16
 4.3 (not for 510, is in 590) 3*, 5*, 6, 8*

5.1
 2*, 3*, 4*, 7, 8, 10, 11
Mon Oct 19
 5.2

3.4
 6*, 14,* 15*, 16*, 17*, 18
Wed Oct 21
HLA example
Fri Oct 23
HLA example
Mon Oct 26 3.5
  4*, 5, 7, 8*, 9*, 11*, 12

7.1
 1*, 3*, 4*, 5*, 6*, 7*, 11*
Wed Oct 28
 7.2
 1*, 2*, 5*, 14, 15, 18
Fri Oct 30
 7.3
 1*, 3*, 4*, 9
Wed Nov 4
 7.4
 1*,  2*,  3
Fri Nov 6
 7.4
 4, 6, 8*, 10, 11, 13
Mon Nov 9
 8.1
  3*, 5,  6*
Wed Nov. 11
 8.1
 7*, 8*, 11, 12, 13, 15
Fri Nov.13
 8.1
 prove the equivalence of 31 and 32 to others (1d, 2 in text)
Mon Nov. 16
 primary decomposition
Wed Nov 18
 linear functionals
 Prove Thm (FDIPS iso)* and Thm (dual basis)* below
Fri Nov 20
 adjoint of transformation
 Ex 2 below
Let A by n x n complex matrix.  Define T_A: C^n -> C^n
by T_A(v)= Av.
Let H be n x n positive definite matrix.  Define inner product <,>_H
on C^n by <x,y>_H = y*Hx.

Nov 18
Thm (FDIPS iso)
Let V, <,> be a FDIPS over C with basis B={v_1,...,v_n}.
Let G=Gram(V_1,...,v_n).
Then the map V -> C^n
                       v -> [v]_B
is a FDIPS isomorphism from V, <,> to C^n, <,>_{G^T}
Thm (dual basis)
Let V, <,> be a FDIPS over C with basis B={v_1,...,v_n}.
Define B*={f_1,...,f_n} where f_i(v_j) = 1 if i=j, 0 if i not j.
Then B* is a basis for V*.

Nov 20
Ex 2
Let H be n x n positive definite matrix. Let B be n x n complex matrix.
Show (T_B)*=T_(H^-1B*H).

Examinations 590LH see alternate assessments except Test 2 is same

Solutions to F09 510 test 1
Test 2 due Friday  Nov  13

Old exams (2006 using same text)

Instructor Information

Leslie HogbenMinnie Catral

Course Information

590LH

590LH text: Applied Linear Algebra by Olver and Shakiban (OS), also Matrix Theory by Fuzhen Zhang (Z)

Reading assignments  (read definitions, statements of theorems, and examples).
    block matrices (Z) 1.2, 2.1
    eigenvalues/vectors (OS) 8.1, 8.2, 8.3, 8.4, (Z) 1.3
    inner produces and orthogonality (OS) 3.1, 3.2; (Z) 1.4; (OS) 5.1, 5.2, 5.3
    commuting matrices (Z) 3.1
    matrix decompositons (Z) 3.1,  (OS) 8.5

590LH graded homework assignment 1 due Fri Sept 18:
(Z) 2.1.2, (Z) 1.3: 11, (OS) 8.2.1(j), 8.2.5, 8.2.20
590LH graded homework assignment 2 due Fri Sept 25:
(OS) 3.1.1, 3.1.3, 3.2.20, 5.3.16(a), #4 on 510 homework 2
590 Homework 3  due WED Oct 21
590 Homework 4 due Friday Nov 20
590 Homework 5 (read OS 4.3 Least Squares) due MON Dec 7

 590LH additional practice/discussion problems (see also * problems on 510):
(Z) 1.2: : 10, 13
(Z) 2.1: 3,  9, 11, 14
(OS) 8.2: 1(e)
(Z) 1.4: 2, 3, 4
(OS) 3.1:3.1.2(a,b,d),
(OS) 5.1: 2, 23
 (OS) 5.2: 1(a)
(OS) 5.3.27(c), 5.3.28(ii)
(OS) 8.5.1(e)(f), 8.5.2(e)(f)

 590LH Test 1 due Monday Oct 5. 
You will be gvien a matirx via e-mail.
1) Find the singular value decompostion of your matrix.
2) Find  QR factorization of your matrix.

 590LH grade based on 5 graded homework (10 points each), takehome tests (test 1, 30 points, is separate takehome, test 2, 70 points, is same as test 2 in 510) and in class 590LH final, 100 points (level of 590LH final will be similar to 590LH homework).



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