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Linear Algebra

Lecture notes 2011 spring semester

 

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    1.1 Vectors and Matrices in Engineering and Mathematics; n-Space

    1.2 Dot Product and Orthogonality

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    7.1 Basis and Dimension

    7.2 Properties of Bases

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    1.2 Dot Product and Orthogonality

    1.3 Vector Equations of Lines and Planes

    2.1 Introduction to Systems of Linear Equations

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    7.2 Properties of Bases

    7.3 The Fundamental Spaces of a Matrix

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    2.1 Introduction to Systems of Linear Equations

    2.2 Solving Linear System by Row Reduction

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    7.3 The Fundamental Spaces of a Matrix

    7.4 The Dimension Theorem and Its Implications

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    2.2 Solving Linear System by Row Reduction

    3.1 Operations on Matrices

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    7.5 The Rank Theorem and Its Implications

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    3.2 Inverses; Algebraic Properties of Matrices

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    7.7 The Projection Theorem and Its Implications

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    3.3 Elementary Matrices; A Method for Finding a Inverses

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    7.9 Orthonormal Bases and the Gram-Schmidt Process

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    3.3 Elementary Matrices; A Method for Finding a Inverse

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    7.11 Coordinates with Respect to a Basis

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    3.4 Subspaces and Linear Independence

    3.5 The Geometry of Linear Systems

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    8.1 Matrix Representations of Linear Transformations

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    3.5 The Geometry of Linear Systems

    3.6 Matrices with Special Forms

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    8.2 Similarity and Diagonalizability

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    4.1 Determinants; Cofactor Expansions

    4.2 Propositions of Determinant

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    8.3 Othogonal Diagonalizability;

    Functions of a Matrix

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    4.3 Cramer's Rule; Formula for a Inverse; Applicaitons for Determinants

    4.4 A First Look at Eigenvalues and Eigenvectors

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    Memorial Day

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    4.4 A First Look at Eigenvalues and Eigenvectors

    6.1 Matrices as Transformations

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    8.4 Quadratic Forms

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    6.2 Geometry of Linear Operators

    6.3 Kernel and Range

    6.4 Composition and Invertibility of

    Transformations

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    8.8 Complex Eigenvalues and Eigenvectors

    8.9 Hermitian, Unitary, and Normal Matrices

 

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    9.1 Vector Space Axioms

    9.2 Inner Product Spaces; Fourier Series

+Mid-term Exam +Final Exam