## Linear Algebra - MTH501 - VU Video Lectures

261 Views
What is Algebra?, What is Linear Algebra?, Applications, Use of linear algebra.
166 Views
Introduction to matrices, Addition, subtraction and multiplication of matrices.
158 Views
System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.
177 Views
Row reduction and Echelon form, Pivot, Row reduction algorithm.
99 Views
Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.
108 Views
Matrix equation.
124 Views
Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.
127 Views
Linear independence.
127 Views
Linear transformations, Transformation.
122 Views
The matrix of a linar transformations.
125 Views
Matrix algebra, Matrix oprations, Diagonal matrix, Zero matrices, Mateix multiplication, Properties of matrix multiplication,Power and Transport of matrix.
80 Views
Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.
86 Views
Charecterizations of invertibe matrices, Invertibe matrix theorem.
124 Views
Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.
100 Views
Matrix factorizations, Matrix inversion.
105 Views
Iterative solution of linear system, Iterative solution, Jacobi's method, Gauss-seidel method, Strictly diagonal dominant.
88 Views
Determinates, Minor of matrix.
111 Views
Properties of determinants.
100 Views
Cramer's rule, Cramer's rule theorem.
152 Views
Vector spaces, Subspaces, Axioms of vector space.
93 Views
Null and Column spaces, Linear transformations.
102 Views
Linearly independent sets;Bases, Spanning set theorem.
84 Views
Coordinate system, Graphical interpretation of coordinates.
112 Views
Dimension of vector space, Bases and Linear combination, Bases theorem.
92 Views
Rank, Row space, Rank theorem, Invertible matrix theorem.
89 Views
Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.
84 Views
Applications to difference equation, Discrete time signal, Linear independence in space of signals, Linear difference equation.
137 Views
Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.
101 Views
Characteristic equation, Properties of determinates, Application to dynamical system.
89 Views
Diagonalization.
86 Views
Eigenvectors and Linear transformations, Matrix of linear transformation.
86 Views
Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.
70 Views
Discrete dynamical systems, Change of variable.
76 Views
Application to difference equation, System of difference equation, Superposition of solutions, Fundamental set, Initial value problem, Decoupling a dynamical system.
93 Views
Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.
78 Views
Characteristic equation, Diagonalization, Eigenvectors and Linear transformations, Complex eigenvalues, Determinant, Minor of matrix, Properties of determinants, Cramer's rule, Volume and Linear transformations.
82 Views
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.
105 Views
Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.
90 Views
Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.
97 Views
Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.
113 Views
Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.
85 Views
Orthogonality and Least square, Least square problem, Least square solution.
87 Views
Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.
144 Views
Application of inner product spaces, Least square line, Weighted Least-squares.
92 Views
Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.