SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION: Recognizing Linear Systems and Solutions. Matrices, Equivalence and Row Operations. Echelon Forms and Gaussian Elimination. Free Variables and General Solutions. The Vector Form of the General Solution. Geometric Vectors and Linear Functions. Polynomial Interpolation. MATRIX NUMBER SYSTEMS: Complex Numbers. Matrix Multiplication. Auxiliary Matrices and Matrix Inverses . Symmetric Projectors, Resolving Vectors . Least Squares Approximation. Changing Plane Coordinates. The Fast Fourier Transform and the Euclidean Algorithm. DIAGONALIZABLE MATRICES: Eigenvectors and Eigenvalues. The Minimal Polynomial Algorithm. Linear Recurrence Relations. Properties of the Minimal Polynomial. The Sequence {Ak}. Discrete Dynamical Systems. Matrix Compression with Components
DETERMINANTS: Area and Composition of Linear Functions. Computing Determinants. Fundamental Properties of Determinants . Further Applications. APPENDIX. SELECTED PRACTICE PROBLEM ANSWERS. INDEX.