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Linear Algebra - MTH501 - VU Video Lectures

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1414 Views
Rated 3
What is Algebra?, What is Linear Algebra?, Applications, Use of linear algebra.
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768 Views
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Introduction to matrices, Addition, subtraction and multiplication of matrices.
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706 Views
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System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
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816 Views
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Row reduction and Echelon form, Pivot, Row reduction algorithm.
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610 Views
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Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
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594 Views
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Matrix equation.
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621 Views
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Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
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613 Views
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Linear independence.
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559 Views
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Linear transformations, Transformation.
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619 Views
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The matrix of a linar transformations.
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603 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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650 Views
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Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
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568 Views
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Charecterizations of invertibe matrices, Invertibe matrix theorem.
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562 Views
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Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
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564 Views
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Matrix factorizations, Matrix inversion.
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599 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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542 Views
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Determinates, Minor of matrix.
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540 Views
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Properties of determinants.
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619 Views
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Cramer's rule, Cramer's rule theorem.
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639 Views
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Vector spaces, Subspaces, Axioms of vector space.
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574 Views
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Null and Column spaces, Linear transformations.
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609 Views
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Linearly independent sets;Bases, Spanning set theorem.
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687 Views
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Coordinate system, Graphical interpretation of coordinates.
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584 Views
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Dimension of vector space, Bases and Linear combination, Bases theorem.
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497 Views
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Rank, Row space, Rank theorem, Invertible matrix theorem.
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569 Views
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Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
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580 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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689 Views
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Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
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570 Views
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Characteristic equation, Properties of determinates, Application to dynamical system.
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513 Views
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Diagonalization.
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529 Views
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Eigenvectors and Linear transformations, Matrix of linear transformation.
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484 Views
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Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
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483 Views
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Discrete dynamical systems, Change of variable.
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588 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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564 Views
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Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
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487 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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456 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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556 Views
Rated 2
Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
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533 Views
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Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
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538 Views
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Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
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469 Views
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Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
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463 Views
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Orthogonality and Least square, Least square problem, Least square solution.
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528 Views
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Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
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527 Views
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Application of inner product spaces, Least square line, Weighted Least-squares.
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506 Views
Rated 2
Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.