Linear Algebra DemystifiedTaught at junior level math courses at every university, Linear Algebra is essential for students in almost every technical and analytic discipline. |
Contents
Chapter 2 Matrix Algebra | 34 |
Chapter 3 Determinants | 59 |
Chapter 4 Vectors | 76 |
Chapter 5 Vector Spaces | 94 |
Chapter 6 Inner Product Spaces | 120 |
Chapter 7 Linear Transformations | 135 |
Chapter 8 The Eigenvalue Problem | 154 |
Chapter 9 Special Matrices | 180 |
Chapter 10 Matrix Decomposition | 199 |
Final Exam | 217 |
Hints and Solutions | 230 |
References | 248 |
Index | 249 |
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Common terms and phrases
augmented matrix basis vectors calculate Cayley-Hamilton Theorem characteristic equation characteristic polynomial coefficient column space column vector complex conjugate complex numbers complex vector space components Consider Cramer's rule Demystified diagonal elements eigenvectors elementary matrix elementary row operations eliminate entry EXAMPLE find a solution Find the determinant Find the eigenvalues Find the matrix Find the row function Gauss–Jordan elimination gives gºv Hermitian conjugate Hermitian matrix identity matrix inner product linear combination linear equations linear system linear transformation linearly independent LU decomposition matrix multiplication matrix representation McGraw-Hill Companies normalized eigenvectors null space number of rows obtain orthogonal orthonormal basis pivot Quiz real numbers reduce the matrix row and column row canonical form row echelon form row space scalar multiplication second row singular value ſº span standard basis subspace system Ax Systems of Linear theorem tr(A unitary matrix value decomposition vector addition write zero vector