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    Matrix Theory Applications and Theorems

    Published 2018
    Subjects: “…2000 ams subject classifications: 15a15, exact finite differences derivative, quaternion matrix, eigenvalues, moore-penrose inverse…”
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    DOAB: description of the publication
    Electronic Book Chapter
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    Fundamentals of Matrix Algebra by Hartman, Gregory

    Published 2011
    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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