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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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278 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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260 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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280 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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192 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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193 Views
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Matrix equation.
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219 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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210 Views
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Linear independence.
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195 Views
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Linear transformations, Transformation.
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208 Views
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The matrix of a linar transformations.
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202 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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168 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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154 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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204 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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183 Views
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Matrix factorizations, Matrix inversion.
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165 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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188 Views
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Determinates, Minor of matrix.
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202 Views
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Properties of determinants.
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210 Views
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Cramer's rule, Cramer's rule theorem.
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226 Views
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Vector spaces, Subspaces, Axioms of vector space.
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173 Views
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Null and Column spaces, Linear transformations.
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189 Views
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Linearly independent sets;Bases, Spanning set theorem.
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172 Views
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Coordinate system, Graphical interpretation of coordinates.
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183 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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165 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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174 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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192 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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195 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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188 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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159 Views
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Diagonalization.
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172 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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165 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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146 Views
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Discrete dynamical systems, Change of variable.
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147 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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197 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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143 Views
Rated 3
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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151 Views
Rated 3
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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185 Views
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Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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174 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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189 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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179 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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140 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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157 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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206 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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174 Views
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Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.