Date

Time

Place

Room

Topics (from Syllabus)

Wednesday, Sept 17

17:0019:00

TUT


1, 2

Thursday, Sept 18

17:0019:00 
TUT


3, 4

Friday, Sept 19

17:0019:00 
UTA


5, 6

Wednesday, Sept 24

17:0019:00 
UTA


7, 8

Thursday, Sept 25

17:0019:00 
UTA


9, 10

Lectures
·
Lecture 1: Preliminaries
·
Lecture 2: Generalized Inverses
·
Lecture 3: Least Squares
·
Lecture 4: Partitioned Matrices and
Determinants
·
Lecture 5: Matrix Volume
·
Illustrations with Maple
(written for Maple12, but should be compatible with older versions of Maple)
·
Lecture 6: The Group Inverse
·
Lecture 7: The Drazin Inverse
·
Lecture 8: The SVDecompoition
·
Lecture 9: Applications to Statistics
·
Lecture 10: Miscellaneous Applications
Reading
list (to be updated):
1.
A. BI, Review of linear
algebra (given in chapter 0 of
this file, that includes also some front matter from the above mentioned text)
2. A. BI, Bibliography
of generalized inverses (2002)
3. A. BI, On error bounds for generalized inverses, SIAM J. Numer. Anal. 3(1966), 585592
4. A. BI, A volume associated with m x n matrices, Lin. Algeb. and its Appl. 167(1992),
87111
5. A. BI, The change of variables formula
using matrix volume, SIAM Journal
on Matrix Analysis 21(1999), 300312
6. A. BI, An application of the matrix volume
in probability, Lin. Algeb.
and its Appl. 321(2001), 925
7. A. BI, The Moore of the MoorePenrose inverse, Electron. J. Lin. Algeb. 9(2002),
150157
8. J.W. Blattner, Bordered matrices, J. Soc. Indust. Appl. Math. 10(1962),
528533
9. F. Burns, D. Carlson, E.
Haynsworth and T. Markham, Generalized
inverse formulas using the Schur complement, SIAM J. Appl. Math. 26(1974),
254259
10.
S.L. Campbell, The Drazin inverse of an
infinite matrix, SIAM J. Appl.
Math. 31(1976), 492503
11.
S.L. Campbell, Index two
linear timevarying singular system of differential equations, SIAM J. Alg. Disc. Meth. 4(1983),
237243
12.
S.L. Campbell, C.D. Meyer and N.J. Rose, Applications of the Drazin inverse to linear
systems of differential equations with singular constant coefficients, SIAM J. Appl. Math. 31(1976),
411425
13.
D. Constales, A closed from formula
for the MoorePenrose inverse of a complex matrix of given rank, Acta Math. Hungar. 80(1998),
8388
14.
M.P. Drazin, Pseudoinverses
in associative rings and semigroups, Amer. Math. Monthly 65(1958), 506514
15.
A. Galantai and Cs. J. Hegedus, Jordan’s principal angles in
complex vector spaces, Numer.
Lin. Algeb. Appl. 13(2006), 589598
16.
T.N.E. Greville, Some
applications of the pseudoinverse of a matrix, SIAM Rev.
2(1960), 1522
17.
P. Kunkel and V. Mehrmann, Generalized inverses of differentialalgebraic
operators, SIAM J. Matrix
Anal. Appl. 17(1996), 426442
18.
Y. Levin and A. BI, A Newton method for systems of m
equations in n variables, Nonlinear
Analysis 47 (2001), 19611971
19.
C.D. Meyer, The
role of the group generalized inverse in the theory of finite Markov chains,
SIAM Rev. 17(1975),
443464
20.
J. Miao and A. BI, On principal angles between
subspaces in R^n, Lin. Algeb.
Appl. 171(1992), 8198
21.
J. Miao and A. BI, On l_p approximate
solutions of linear equations, Lin.
Algeb. Appl. 199(1994), 305327
22.
W.T. Reid, Generalized
Green’s matrices for twopoint boundary problems, SIAM J. Appl. Math. 15(1967),
856870
23.
A. Rieder and T. Schuster, The approximate inverse in action with an application
to computerized tomography, SIAM
J. Numer. Anal. 37(2000), 19091929
24.
C.F. Van Loan, Generalizing
the SVD, SIAM J. Numer. Anal. 13(1976),
7683