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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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424 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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404 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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441 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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335 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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314 Views
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Matrix equation.
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336 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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325 Views
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Linear independence.
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294 Views
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Linear transformations, Transformation.
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353 Views
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The matrix of a linar transformations.
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329 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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313 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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294 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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315 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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291 Views
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Matrix factorizations, Matrix inversion.
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265 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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275 Views
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Determinates, Minor of matrix.
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288 Views
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Properties of determinants.
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338 Views
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Cramer's rule, Cramer's rule theorem.
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348 Views
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Vector spaces, Subspaces, Axioms of vector space.
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297 Views
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Null and Column spaces, Linear transformations.
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289 Views
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Linearly independent sets;Bases, Spanning set theorem.
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283 Views
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Coordinate system, Graphical interpretation of coordinates.
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289 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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241 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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278 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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319 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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298 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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295 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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220 Views
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Diagonalization.
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261 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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241 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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232 Views
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Discrete dynamical systems, Change of variable.
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246 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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305 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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222 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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223 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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298 Views
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Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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278 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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298 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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241 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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209 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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236 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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288 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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266 Views
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Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.