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] 2.12.4 
Th. 1/31 
Sums and direct sums of vector spaces. Block matrices. 
[A] Ch. 2, 3. [S] 2.12.4 
Tu. 2/5  Orthogonality, CauchySchwarz, orthogonal spaces.  [S] 3.13 
Th. 2/7  Nearest solution to a system  [S] 3.13 
Tu. 2/12  GramSchmidt 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] 1.12 
Th. 4/11  Hermitian matrices. Normal matrices. 
[H] 4.01, 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] 8.02 
Th. 4/30  Positive and nonnegative matrices.  [H] 8.02 
Th. 5/2  Positive and nonnegative matrices.  [H] 8.02 
Tu. 5/7  Questions? 