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Linear Algebra - MTH501 - VU Video Lectures

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What is Algebra?, What is Linear Algebra?, Applications, Use of linear algebra.
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166 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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158 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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177 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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99 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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108 Views
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Matrix equation.
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124 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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127 Views
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Linear independence.
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127 Views
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Linear transformations, Transformation.
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122 Views
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The matrix of a linar transformations.
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125 Views
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Matrix algebra, Matrix oprations, Diagonal matrix, Zero matrices, Mateix multiplication, Properties of matrix multiplication,Power and Transport of matrix.
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80 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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86 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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124 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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100 Views
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Matrix factorizations, Matrix inversion.
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105 Views
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Iterative solution of linear system, Iterative solution, Jacobi's method, Gauss-seidel method, Strictly diagonal dominant.
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88 Views
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Determinates, Minor of matrix.
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111 Views
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Properties of determinants.
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100 Views
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Cramer's rule, Cramer's rule theorem.
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152 Views
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Vector spaces, Subspaces, Axioms of vector space.
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93 Views
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Null and Column spaces, Linear transformations.
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102 Views
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Linearly independent sets;Bases, Spanning set theorem.
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84 Views
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Coordinate system, Graphical interpretation of coordinates.
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112 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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92 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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89 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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84 Views
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Applications to difference equation, Discrete time signal, Linear independence in space of signals, Linear difference equation.
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137 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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101 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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89 Views
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Diagonalization.
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86 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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86 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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70 Views
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Discrete dynamical systems, Change of variable.
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76 Views
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Application to difference equation, System of difference equation, Superposition of solutions, Fundamental set, Initial value problem, Decoupling a dynamical system.
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93 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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78 Views
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Characteristic equation, Diagonalization, Eigenvectors and Linear transformations, Complex eigenvalues, Determinant, Minor of matrix, Properties of determinants, Cramer's rule, Volume and Linear transformations.
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82 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system, Row reduction and echelon form, Row reduction algorithm, Vector equations, Matrix equation, Trivial solution, Non trivial solution, Linear independence, Linear transformations.
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105 Views
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Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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90 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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97 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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113 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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85 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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87 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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144 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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92 Views
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Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.