Fundamentals of Matrix Algebra by Hartman, Gregory

Table of Contents: “…1 Systems of Linear Equations -- 1.1 Introduction to Linear Equations -- 1.2 Using Matrices To Solve Systems of Linear Equations -- 1.3 Elementary Row Operations and Gaussian Elimination -- 1.4 Existence and Uniqueness of Solutions -- 1.5 Applications of Linear Systems -- 2 Matrix Arithmetic -- 2.1 Matrix Addition and Scalar Multiplication -- 2.2 Matrix Multiplication -- 2.3 Visualizing Matrix Arithmetic in 2D -- 2.4 Vector Solutions to Linear Systems -- 2.5 Solving Matrix Equations AX = B -- 2.6 The Matrix Inverse -- 2.7 Properties of the Matrix Inverse -- 3 Operations on Matrices -- 3.1 The Matrix Transpose -- 3.2 The Matrix Trace -- 3.3 The Determinant -- 3.4 Properties of the Determinant -- 3.5 Cramer’s Rule -- 4 Eigenvalues and Eigenvectors -- 4.1 Eigenvalues and Eigenvectors -- 4.2 Properties of Eigenvalues and Eigenvectors -- 5 Graphical Explorations of Vectors -- 5.1 Transformations of the Cartesian Plane -- 5.2 Properties of Linear Transformations -- 5.3 Visualizing Vectors: Vectors in Three Dimensions…”
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Mathematics of Economics and Business by Werner, Frank

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Mathematics of Economics and Business by Werner, Frank

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Tea Time Linear Algebra Explorations in Mathematics by Brin, Leon Q.

Table of Contents: “…Preface -- I. Matrix Mechanics -- 1. Matrix Calculations -- 2. Row Operations -- 3. …”
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Algorithms for Sparse Linear Systems by Scott, Jennifer, Tůma, Miroslav

Table of Contents: “…An introduction to sparse matrices -- Sparse matrices and their graphs -- Introduction to matrix factorizations -- Sparse Cholesky sovler: The symbolic phase -- Sparse Cholesky solver: The factorization phase -- Sparse LU factorizations -- Stability, ill-conditioning and symmetric indefinite factorizations -- Sparse matrix ordering algorithms -- Algebraic preconditioning and approximate factorizations -- Incomplete factorizations -- Sparse approximate inverse preconditioners.…”
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Applied Discrete Structures by Doerr, Alan, Levasseur, Kenneth

Table of Contents: “…1 Set Theory -- 2 Combinatorics -- 3 Logic -- 4 More on Sets -- 5 Introduction to Matrix Algebra -- 6 Relations and Graphs -- 7 Functions -- 8 Recursion and Recurrence Relations -- 9 Graph Theory -- 10 Trees -- 11 Algebraic Systems -- 12 More Matrix Algebra -- 13 Boolean Algebra -- 14 Monoids and Automata -- 15 Group Theory and Applications -- 16 An Introduction to Rings and Fields…”
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Introduction to Systems Biology Workbook for Flipped-Classroom Teaching by Sauter, Thomas, Albrecht, Marco

Table of Contents: “…Preface -- Introduction -- Chapter 1: Biochemcial networks in the matrix form -- Chapter 2: Metabolic modeling -- Chapter 3: the magic of change and how to find itt -- Chapter 4: Physical modeling and non-linear enzyme…”
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A First Course in Linear Algebra by Kuttler, Ken

Table of Contents: “…1 Systems of Equations -- 1.1 Systems of Equations, Geometry -- 1.2 Systems Of Equations, Algebraic Procedures -- 2 Matrices -- 2.1 Matrix Arithmetic -- 2.2 LU Factorization -- 3 Determinants -- 3.1 Basic Techniques and Properties -- 3.2 Applications of the Determinant -- 4 R^n -- 4.1 Vectors in R^n -- 4.2 Algebra in R^n -- 4.3 Geometric Meaning of Vector Addition -- 4.4 Length of a Vector -- 4.5 Geometric Meaning of Scalar Multiplication -- 4.6 Parametric Lines -- 4.7 The Dot Product -- 4.8 Planes in R^n -- 4.9 The Cross Product -- 4.10 Spanning, Linear Independence and Basis in R^n -- 4.11 Orthogonality and the Gram Schmidt Process -- 4.12 Applications -- 5 Linear Transformations -- 5.1 Linear Transformations -- 5.2 The Matrix of a Linear Transformation I -- 5.3 Properties of Linear Transformations -- 5.4 Special Linear Transformations in R^2 -- 5.5 One to One and Onto Transformations -- 5.6 Isomorphisms -- 5.7 The Kernel And Image Of A Linear Map -- 5.8 The Matrix of a Linear Transformation II -- 5.9 The General Solution of a Linear System -- 6 Complex Numbers -- 6.1 Complex Numbers -- 6.2 Polar Form -- 6.3 Roots of Complex Numbers -- 6.4 The Quadratic Formula -- 7 Spectral Theory -- 7.1 Eigenvalues and Eigenvectors of a Matrix -- 7.2 Diagonalization -- 7.3 Applications of Spectral Theory -- 7.4 Orthogonality -- 8 Some Curvilinear Coordinate Systems -- 8.1 Polar Coordinates and Polar Graphs -- 8.2 Spherical and Cylindrical Coordinates -- 9 Vector Spaces -- 9.1 Algebraic Considerations -- 9.2 Spanning Sets -- 9.3 Linear Independence -- 9.4 Subspaces and Basis -- 9.5 Sums and Intersections -- 9.6 Linear Transformations -- 9.7 Isomorphisms -- 9.8 The Kernel And Image Of A Linear Map -- 9.9 The Matrix of a Linear Transformation -- A Some Prerequisite Topics -- A.1 Sets and Set Notation -- A.2 Well Ordering and Induction -- B Selected Exercise Answers…”
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Abstract Algebra Theory and Applications by Judson, Thomas W.

Table of Contents: “…Preliminaries -- The Integers -- Groups -- Cyclic Groups -- Permutation Groups -- Cosets and Lagrange's Theorem -- Introduction to Cryptography -- Algebraic Coding Theory -- Isomorphisms -- Normal Subgroups and Factor Groups -- Homomorphisms -- Matrix Groups and Symmetry -- The Structure of Groups -- Group Actions -- The Sylow Theorems -- Rings -- Polynomials -- Integral Domains -- Lattices and Boolean Algebras -- Vector Spaces -- Fields -- Finite Fields -- Galois Theory…”
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Linear Algebra with Applications by Nicholson, W. Keith

Table of Contents: “…1 Systems of Linear Equations -- 2 Matrix Algebra -- 3 Determinants and Diagonalization -- 4 Vector Geometry -- 5 Vector Space R -- 6 Vector Spaces -- 7 Linear Transformations -- 8 Orthogonality -- 9 Change of Basis -- 10 Inner Product Spaces -- 11 Canonical Forms -- A Complex NumbersB ProofsC Mathematical InductionD PolynomialsSelected Exercise Answers…”
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Open Logic Project by Zach, Richard, Arana, Andrew, Avigad, Jeremy, Dean, Walter, Russell, Gillian, Wyatt, Nicole, Yap, Audrey

Table of Contents: “…I Naıve Set Theory -- II Propositional Logic -- III First-order Logic -- IV Model Theory -- V Computability -- VI Turing Machines -- VII Incompleteness -- VIII Second-order Logic -- IX The Lambda Calculus -- X Many-valued Logic -- XI Normal Modal Logics -- XII Intuitionistic Logic -- XIII Counterfactuals -- XIV Set Theory -- XV Methods -- XVI History…”
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Applied Combinatorics by Keller, Mitchel T., Trotter, William T.

Table of Contents: “…Polya's Enumeration Theorem -- 16. The Many Faces of Combinatorics -- A. Epilogue -- B. …”
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Introductory Business Statistics by Tiemann, Thomas K.

Table of Contents: “…Some non-parametric tests -- Do these populations have the same location? The Mann-Whitney U testTesting with matched pairs: the Wilcoxon signed ranks test. -- Are these two variables related? …”
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Introduction to GNU Octave A brief tutorial for linear algebra and calculus students by Lachniet, Jason

Table of Contents: “…Contents -- Preface -- 1 Basic operation -- 1.1 Introduction -- 1.2 Navigating the GUI -- 1.3 Matrices and vectors -- 1.4 Plotting -- Chapter 1 Exercises -- 2 Matrices and linear systems -- 2.1 Linear systems -- 2.2 Polynomial curve fitting -- 2.3 Matrix transformations -- Chapter 2 Exercises -- 3 Calculus -- 3.1 Limits, sequences, and series -- 3.2 Numerical integration -- 3.3 Parametric, polar, and implicit functions -- 3.4 Complex variables -- 3.5 Special functions -- 3.6 Symbolic operations -- Chapter 3 Exercises -- 4 Eigenvalue problems -- 4.1 Eigenvalues and eigenvectors -- 4.2 Markov chains -- 4.3 Diagonalization -- 4.4 Singular value decomposition -- 4.5 Gram-Schmidt and the QR algorithm -- Chapter 4 Exercises -- 5 Additional topics -- 5.1 Three dimensional graphs -- 5.2 Multiple integrals -- 5.3 Vector fields -- 5.4 Statistics -- 5.5 Differential equations -- Chapter 5 Exercises -- 6 Applied projects -- 6.1 SVD and digital image compression -- 6.2 The Gini index and nonlinear curve-fitting -- 6.3 Designing a helical strake: arc length and curvature -- 6.4 Modeling a cave passage: cubic spline curves -- 6.5 Graphs of surfaces and 3D-printing -- A MATLAB compatibility -- B List of Octave commands -- References -- Index…”
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College Algebra 2e by Abramson, Jay

Table of Contents: “…Systems of Equations and Inequalities -- Introduction to Systems of Equations and Inequalities -- 7.1 Systems of Linear Equations: Two Variables -- 7.2 Systems of Linear Equations: Three Variables -- 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables -- 7.4 Partial Fractions -- 7.5 Matrices and Matrix Operations -- 7.6 Solving Systems with Gaussian Elimination -- 7.7 Solving Systems with Inverses -- 7.8 Solving Systems with Cramer's Rule -- Chapter Review -- Exercises -- Chapter 8. …”
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Proof and Proving in Mathematics Education The 19th ICMI Study /

Table of Contents: “…Transitions and proof and proving at tertiary level: Annie Selden -- Part VI: Lessons from the Eastern cultural traditions -- 18. …”
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Algebra and Trigonometry 2e by Abramson, Jay

Table of Contents: “…Systems of Equations and Inequalities -- Introduction to Systems of Equations and Inequalities -- 11.1 Systems of Linear Equations: Two Variables -- 11.2 Systems of Linear Equations: Three Variables -- 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables -- 11.4 Partial Fractions -- 11.5 Matrices and Matrix Operations -- 11.6 Solving Systems with Gaussian Elimination -- 11.7 Solving Systems with Inverses -- 11.8 Solving Systems with Cramer's Rule -- Chapter Review -- Exercises -- Chapter 12. …”
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Linear Algebra, Theory And Applications by Kuttler, Kenneth

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Intermediate Algebra by Redden, John

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Advanced Algebra by Redden, John

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