Kent Pearce -- Review: Math 2360-20084(002)

Kent Pearce

Department of Mathematics and Statistics
Texas Tech University
Lubbock, Texas 79409-1042
Voice: (806)742-2566 x 226
FAX: (806)742-1112
Email: kent.pearce@ttu.edu

Math 2360
Linear Algebra
Summer II 2008

Leon, Steven J
Linear Algebra
Pearson

Review Exam IV

Section	Content	Suggested Problems
Section 5.1	Scalar product of vectors in Rⁿ Length of a vector in in Rⁿ Distance between two vectors in in Rⁿ Angle between two vectors in Rⁿ Cauchy-Schwarz Inequality Definition of orthogonality for vectors in Rⁿ Projections Vector projection of x onto y Scalar rojection of x onto y	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13,
Section 5.2	Orthogonal subspaces Orthogonal complement of a subspace Theorem 5.2.1 Fundamental Subspaces Theorem Direct sum of subspaces Theorem 5.2.3	1, 2, 4, 5,
Section 5.3	Least Square Problem for Ax = b Theorem 5.3.1 Normal Equations for Least Squares Problem Theorem 5.3.2 Least squares soluton for matrix A with rank n	1a, 1b, 2
Section 5.5	Orthogonal set Orthonormal set Theorem 5.5.1 Theorem 5.5.2 Coordinates computations for orthonormal bases Orthogonal matrix Properties of orthogonal matrices Theorem 5.5.7 Projection onto a subspace with an orthonormal basis	1, 2, 3, 21
Section 5.6	Theorem 5.6.1 Gram-Schmidt Orthogonalization Process Theorem 5.6.2 Gram-Schmidt QR Factorization Theorem 5.6.3 Least squares solution for matrix A with rank n via QR factorizaton	1, 2, 3, 5, 8
Section 6.1	Eigenvector Eignenvalue Characteristic polynomial Complex eigenvalues and eigenvectors of real matrices Compute eigenvalues and eigenvectors Product and sum of eigenvalues Eigenvalues of upper triangular matrix Eigenvalues of similar matrices	1, 2, 11
Section 6.3	Diagonalizable Theorem 6.3.2 Arithmetic Multiplicity vs Geometric Multiplicity	1, 2

Comments maybe be mailed to: kent.pearce@ttu.edu

Last modified on: Monday, 10-Aug-2015 12:47:29 CDT