Transform Linear Algebra
First Edition

by Frank Uhlig

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Select a section: Section 1.1 Lecture One: Vectors, Linear Functions, and Matrices Section 1.2 Tasks and Methods of Linear Algebra Section 1.3 Applications: Geometry, Calculus, and MATLAB Section 2.1 Lecture Two: Gaussian Elimination and the Echelon Forms Section 2.2 Applications: MATLAB Section 3.1 Lecture Three: Solvability and Solutions of Linear Systems Section 3.2 Applications: Circuits, Networks, Chemistry, and MATLAB Section 4.1 Lecture Four: The Image and Kernel of a Linear Transformation Section 4.2 Applications: Join and Intersection of Subspaces Section 5.1 Lecture Five: Minimal Spanning or Maximally Independent Sets of Section 5.2: Applications Multiple Spanning Sets of One Subspace, MATLAB Section 6.1 Lecture Six Section 6.2 Theory: Gaussian Elimination Matrix Products, the Uniqueness of the Section 6.3 Applications: MATLAB Section 7.1 Lecture Seven: Matrix Representations with respect to General Bases Section 7.2 Theory: Rank, Matrix Transpose Section 7.3: Applications Subspace Basis Change, Calculus Section 8.1 Lecture Eight: Laplace Expansion, Gaussian Elimination, and Properties Section 8.2: Theory: Axiomatic Definition Section 8.3: Applications: Volume Wronskian Section 9.1 Lecture Nine, Using Vector Iteration: Vanishing and Minimal Polynomial, Section 9.2: Theory: Geometry, Vector Iteration, and Eigenvalue Functions Section 9.3 Applications: Stochastic Matrices, Systems of Linear DE's and MATLAB Section 10.1 Lecture Ten: Length, Orthogonality, and Orthonormal Bases Section 10.2: Theory: Matrix Generation, Rank 1 and Householder Matrices Section 10.3 Applications: QR Decomposition, MATLAB, and Least Squares Section 11.1 Lecture Eleven: Matrix Representations with respect to One Orthonormal Section 11.2 Theory: Normal Matrices Section 11.3 Applications: Polar Decomposition, Volume, ODEs, and Quadrics Section 12.1 Lecture Twelve: Matrix Representations with respect to Two Orthonormal Section 12.2 Theory: Matrix Approximation, Least Squares Section 12.3 Applications: Geometry, Data Compression, Least Squares, and MATLAB Section 13.1 Lecture Thirteen: Computer Arithmetic, Stability, and the QR Algorithm