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 WelcomeTable of Contents Chapter 1: Matrices and Systems of Equations     Section 1.1: Systems of Linear Equations     Section 1.2: Row Echelon Form     Section 1.3: Matrix Algebra     Section 1.4 Elementary Matrices     Section 1.5: Partitioned Matrices Chapter 2: Determinants     Section 2.1: The Determinant of a Matrix     Section 2.2: Properties of Determinants     Section 2.3: Cramer's Rule Chapter 3: Vector Spaces     Section 3.1 Definition and Examples     Section 3.2: Subspaces     Section 3.3: Linear Independence     Section 3.4: Basis and Dimension     Section 3.5: Change of Basis     Section 3.6: Row Space and Column Space Chapter 4: Linear Transformations     Section 4.1: Linear Transformations: Def     Section 4.2: Matrix Representations of L     Section 4.3: Similarity Chapter 5: Orthogonality     Section 5.1: The Scalar Product in R     Section 5.2: Orthagonal Subspaces     Section 5.3: Least Squares Problems     Section 5.4: Inner Product Spaces     Section 5.5: Orthonormal Sets     Section 5.6: The Gram-Schmidt Orthogonal     Section 5.7: Orthogonal Polynomials Chapter 6: Eigenvalues     Section 6.1: Eigenvalues and Eigenvector     Section 6.2: Systems of Linear Different     Section 6.3: Diagonalization     Section 6.4: Hermitian Matrices     Section 6.5: The Singular Value Decomposition     Section 6.6: Quadratic Forms     Section 6.7: Positive Definite Matrices     Section 6.8: Nonnegative Matrices Chapter 7: Numerical Linear Algebra    Chapter 1: Section 7.1: Floating-Point Numbers    Chapter 2: Section 7.2: Gaussian Elimination    Chapter 3: Section 7.3: Pivoting Strategies    Chapter 4: Section 7.4: Matrix Norms and Condition Numbers    Chapter 5: Section 7.5: Orthogonal Transformations    Chapter 6: Section 7.6: The Eigenvalue Problem    Chapter 7: Section 7.7: Least Squares Problems Chapter 8: Iterative Methods        Author's Website    ATLAST Project Chapter 9: Canonical Forms        Author's Website    ATLAST Project