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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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214 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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204 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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222 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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140 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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134 Views
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Matrix equation.
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166 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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165 Views
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Linear independence.
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152 Views
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Linear transformations, Transformation.
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141 Views
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The matrix of a linar transformations.
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158 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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118 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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119 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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154 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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135 Views
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Matrix factorizations, Matrix inversion.
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128 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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124 Views
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Determinates, Minor of matrix.
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144 Views
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Properties of determinants.
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144 Views
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Cramer's rule, Cramer's rule theorem.
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187 Views
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Vector spaces, Subspaces, Axioms of vector space.
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121 Views
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Null and Column spaces, Linear transformations.
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130 Views
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Linearly independent sets;Bases, Spanning set theorem.
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121 Views
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Coordinate system, Graphical interpretation of coordinates.
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139 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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119 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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124 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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129 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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158 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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128 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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114 Views
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Diagonalization.
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117 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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124 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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105 Views
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Discrete dynamical systems, Change of variable.
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111 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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127 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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108 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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114 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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139 Views
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Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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130 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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129 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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148 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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112 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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112 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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172 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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125 Views
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Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.