Math 623: Matrix Analysis
Spring 2013

Instr: Mike O'Sullivan


Schedule

I will try to keep to this schedule but will update it as needed.
References are

[HJ] Horn, Johnson Matrix Analysis Cambridge University Press, 1st Ed. (1985) or 2nd Ed. (2012).

[S] Strang, Linear Algebra and Its Applications Any edition.

[A] Axler, Linear Algebra Done Right, Springer.


Day Topics Reference
Th. 1/17 From solution of a linear system
to matrix algebra.
Tu. 1/22 Gaussian elimination and elementary matrices. The LU factorization of a matrix.
Th. 1/24 Vector spaces, subspaces, bases.
Tu. 1/29 Matrices for change of bases.
Matrices for linear transformations. 		[A] Ch. 2, 3.
[S] 2.1-2.4
Th. 1/31 Sums and direct sums of vector spaces.
Block matrices. 		[A] Ch. 2, 3.
[S] 2.1-2.4
Tu. 2/5 Orthogonality, Cauchy-Schwarz, orthogonal spaces. [S] 3.1-3
Th. 2/7 Nearest solution to a system [S] 3.1-3
Tu. 2/12 Gram-Schmidt and the QR factorization.
Inner product spaces. 		[S] 3.3
Th. 2/14 Orthogonal matrices and unitary matrices. [S] 3.3 [H] 2.1
Tu. 2/19 Properties of linear transformations
Polynomials and linear transformations		 [A] Ch 5 , [H] 1.1
Th. 2/21 Invariant subspaces.
Eigenvalues, eignevectors and eigenspaces.		 [A] Ch 5,8
Tu. 2/26 Diagonalizable matrices.
Diagonalizable matrices that commute.		 [H] Sec. 1.3
Th. 2/28 Smith Normal from. .
Tu. 3/5 Generalized eigenspace.
Jordan canonical form.		 [A] Ch 8
Th. 3/7 Nilpotent matrices and Jrodan From [A] Ch. 8
Tu. 3/12 Krylow space method.
Companion matrix to a polynomial.		 [H] Sec 3.3.12
Th. 3/14 Real Jordan form
Real Schur triangularization.		 [H] Sec 3.4
2.3.4
Tu. 3/19 Gersgorin discs. 6.1,2
Th. 3/21 . .
Tu. 3/26 Questions??
Some problems.		 .
Th. 3/28 TEST. See review sheet
Tu. 4/9 Determinant, trace and the characteristic polynomial. [A] Ch. 10, [H] 1.1-2
Th. 4/11 Hermitian matrices.
Normal matrices.		 [H] 4.0-1, 2.5
Tu. 4/16 Normal matrices.
The Spectral Theorem		 [H] 2.5
Th. 4/18 Normal matrices.
The Singular Value Decomposition.		 [H] 2.6
Tu. 4/23 Unitary similarity,
miscellaneous topics.		 [H] 2.2, 2.1 Thm 2.1.9
Th. 4/25 Problems on Hermitian and normal matrices. [H] 8.0-2
Th. 4/30 Positive and nonnegative matrices. [H] 8.0-2
Th. 5/2 Positive and nonnegative matrices. [H] 8.0-2
Tu. 5/7 Questions?