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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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333 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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314 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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316 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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223 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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227 Views
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Matrix equation.
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251 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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239 Views
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Linear independence.
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219 Views
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Linear transformations, Transformation.
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249 Views
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The matrix of a linar transformations.
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227 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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217 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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189 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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232 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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215 Views
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Matrix factorizations, Matrix inversion.
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187 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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207 Views
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Determinates, Minor of matrix.
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217 Views
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Properties of determinants.
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227 Views
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Cramer's rule, Cramer's rule theorem.
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252 Views
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Vector spaces, Subspaces, Axioms of vector space.
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196 Views
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Null and Column spaces, Linear transformations.
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220 Views
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Linearly independent sets;Bases, Spanning set theorem.
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183 Views
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Coordinate system, Graphical interpretation of coordinates.
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209 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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179 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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207 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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224 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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220 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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215 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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168 Views
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Diagonalization.
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197 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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196 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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163 Views
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Discrete dynamical systems, Change of variable.
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172 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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228 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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165 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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177 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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202 Views
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Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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195 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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215 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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196 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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158 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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177 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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228 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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188 Views
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Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.