Subjects for final examination

The examination is not comprehensive but focuses
on the material covered after the second midterm.
Of course, I assume that you are knowledgable about
the general notions used in class, like nullspace,
REF, determinant, etc.


-- Scalar products and inner products
   Practice problems: Ch5Sec2Ex6, Ch5Sec2Ex16 (difficult)

-- Normed vector spaces

-- Cauchy-Schwarz inequality and application to norm induced by inner prod
   Practice problems: Ch5Sec3Ex2, Ch5Sec3Ex26

-- Least squares problems I: solution based on linear system solving
   Practice problems: Ch5Sec4Ex9 (moderately difficult)

-- Orthonormal sets and the Gram-Schmidt process
   Least squares problems II: solution based on orthogonalization
   Practice problems: Ch5Sec5Ex13, Ch5Sec6Ex5

-- Eigen-values, -vectors, -spaces; char polynomial
   Practice problems: Ch6Sec1Ex9, Ch6Sec1Ex15
 
-- Solution of lin diff equs with constant coefficients
   Practice problems: Ch6Sec2Ex5

-- Diagonalizing a matrix with lin. ind. eigenvectors
   Practice problems: Ch6Sec3Ex11 (was drill on HW 11)
 
-- Computing a matrix power and the exponential of a matrix
   Practice problems: Ch6Sec3Ex21

-- Complex matrices: conjugate and the Hermitian property
   Practice problems: Ch6Sec4Ex5(d)


Note: You are allowed to bring TWO 8.5' by 11' sheets
with notes on both sides to the exam.