Matrix Theory, Math6304
Lecture Notes from Sept 11, 2012
taken by Tristan Whalen
1
Further Review continued
Warm-up
Let A, B Mn and suppose det(A) = 0. Dene a matrix valued function as follows:
F (t)
Matrix Theory, Math6304
Lecture Notes from October 02, 2012
taken by Sanat Kumar Upadhyay
Last time 09/27/2012
Review
Real matrices
Warm up:
Let O Mn (R) be an orthogonal matrix (i.e. a rotation matri
Matrix Theory, Math6304
Lecture Notes from September 27, 2012
taken by Tasadduk Chowdhury
Last Time (09/25/12):
QR factorization: any matrix A Mn has a QR factorization: A = QR, where Q is unitary
and
Matrix Theory, Math6304
Lecture Notes from October 4, 2012
taken by Yuricel Mondragn
o
Last Time (10/2/12):
Amendment
We should clean up the proof of the basis property from last time. To see that Bj
Matrix Theory, Math6304
Lecture Notes from October 9, 2012
taken by Charles Mills
Last Time (10/6/12)
Suppose A Mn satises A = A , then given A, we can dene a map qA : Cn R by
qA (x) =< Ax, x > . It i
Matrix Theory, Math6304
Lecture Notes from October 23, 2012
taken by Satish Pandey
Warm up from last time
Example of low rank perturbation; re-examined
We had this operator
1
0
. .
.
.
S=
Mn ( C)
.
.
Matrix Theory, Math6304
Lecture Notes from October 16, 2012
taken by Ricky Ng
4.3
Estimation of eigenvalues for sums of Hermitian matrices (continued)
Last time we saw some useful applications of the
Matrix Theory, Math6304
Lecture Notes from October 11, 2012
taken by Da Zheng
4
Variational characterization of eigenvalues, continued
We recall from last class that given a Hermitian matrix, we can o
Matrix Theory, Math6304
Lecture Notes from September 25, 2012
taken by Katie Watkins
Last Time (9/20/12)
Cayley Hamilton
Block diagonalization with triangular blocks
Nearly Diagonalizability
Q: We
Matrix Theory, Math6304
Lecture Notes from September 20, 2012
taken by Ilija Jegdic
Last Class
Unitary diagonalization and normality
Warm up
If A is normal, and A = B + iC , B = B , C = C what we can
Matrix Theory, Math6304
Lecture Notes from August 30, 2012
taken by Andy Chang
Last Time (8/28/12)
Course info: website - math.uh.edu/bgb
Matrix multiplication: left (premultiplication) and right (pos
Matrix Theory, Math6304
Lecture Notes from August 28, 2012
taken by Bernhard Bodmann
0
Course Information
Text: R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 1885.
Oce: PGH 604,
Matrix Theory, Math6304
Lecture Notes from September 4, 2012
taken by Thomas Weber
Last Time (8/30/12)
Gram-Schmidt: - set of linearly independent vectors can yield an orthonormal set that spans
the s
Matrix Theory, Math6304
Lecture Notes from September 6, 2012
taken by Nathaniel Hammen
Last Time (9/4/12)
Diagonalization: conditions for diagonalization
Eigenvalue Multiplicity: algebraic and geometr
Matrix Theory, Math6304
Lecture Notes from September 18, 2012
taken by John Haas
Last Time (9/13/12)
Unitary Matrices: denition and some characterizations/results
Householder Transforms : basic comput
Matrix Theory, Math6304
Lecture Notes from September 13, 2012
taken by Manisha Bhardwaj
Last Time (9/11/12)
Invariant Subspaces: denition
Commuting families: eigenspaces and simultaneous diagonalizati
Matrix Theory, Math6304
Lecture Notes from October 30, 2012
taken by Thomas Weber
Last Time (10/25/12)
Eigenvalue interlacing: general eigenvalue interlacing for principal submatrices
Rayleigh-Ritz pr