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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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604 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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555 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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612 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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472 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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446 Views
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Matrix equation.
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464 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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454 Views
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Linear independence.
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428 Views
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Linear transformations, Transformation.
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484 Views
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The matrix of a linar transformations.
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462 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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468 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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419 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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433 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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419 Views
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Matrix factorizations, Matrix inversion.
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428 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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396 Views
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Determinates, Minor of matrix.
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412 Views
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Properties of determinants.
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474 Views
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Cramer's rule, Cramer's rule theorem.
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485 Views
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Vector spaces, Subspaces, Axioms of vector space.
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422 Views
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Null and Column spaces, Linear transformations.
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431 Views
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Linearly independent sets;Bases, Spanning set theorem.
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486 Views
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Coordinate system, Graphical interpretation of coordinates.
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429 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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357 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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401 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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428 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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466 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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415 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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352 Views
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Diagonalization.
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373 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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344 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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338 Views
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Discrete dynamical systems, Change of variable.
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419 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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424 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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346 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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330 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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433 Views
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Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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392 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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415 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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355 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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308 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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365 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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407 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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383 Views
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Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.