Mathematics & Statistics Texas Tech University 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

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