1867 Views

What is Algebra?, What is Linear Algebra?, Applications, Use of linear algebra.

1227 Views

Introduction to matrices, Addition, subtraction and multiplication of matrices.

1075 Views

System of linear equations, Example of linear equations, Homogenous linear equations, Linear system.

1198 Views

Row reduction and Echelon form, Pivot, Row reduction algorithm.

968 Views

Vector equations, Algebra of vector, Algebric propeoties, Linear combination, Vector and Parametric equation of line.

1048 Views

Solution set of linear system,Homogenous linear systems, Trivial solution, Non trivial solution.

973 Views

Matrix algebra, Matrix oprations, Diagonal matrix, Zero matrices, Mateix multiplication, Properties of matrix multiplication,Power and Transport of matrix.

1197 Views

Matrix algebra, Inverse of matrix, Inverse of transport and Product, Inverse operations.

1002 Views

Charecterizations of invertibe matrices, Invertibe matrix theorem.

988 Views

Partitioned matrices, Addition and Scaler multiplication, Column-row expansion theorem, Inverse of partitioned matrices.

1441 Views

Iterative solution of linear system, Iterative solution, Jacobi's method, Gauss-seidel method, Strictly diagonal dominant.

1048 Views

Linearly independent sets;Bases, Spanning set theorem.

1256 Views

Coordinate system, Graphical interpretation of coordinates.

1037 Views

Dimension of vector space, Bases and Linear combination, Bases theorem.

880 Views

Rank, Row space, Rank theorem, Invertible matrix theorem.

972 Views

Dimension, Chang of basis, Axioms of vector space, Linearly independent, Linearly dependent.

925 Views

Applications to difference equation, Discrete time signal, Linear independence in space of signals, Linear difference equation.

1117 Views

Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.

978 Views

Characteristic equation, Properties of determinates, Application to dynamical system.

875 Views

Eigenvectors and Linear transformations, Matrix of linear transformation.

901 Views

Complex eigen-values, Real and Imaginary parts of vectors, Eigenvalues and Eigenvectors of real vectors.

1519 Views

Application to difference equation, System of difference equation, Superposition of solutions, Fundamental set, Initial value problem, Decoupling a dynamical system.

979 Views

Iterative estimates for eigenvalues, Power method, Inverse Power method, Diagonalization theorem, Eigenvectors and Linear transformations.

839 Views

Characteristic equation, Diagonalization, Eigenvectors and Linear transformations, Complex eigenvalues, Determinant, Minor of matrix, Properties of determinants, Cramer's rule, Volume and Linear transformations.

786 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.

940 Views

Orthogonality and Least square, Inner product,Length and Orthogonality, Unit vector, Pythagoren theorem, Orthogonal complement.

864 Views

Orthogonal sets, Orthogonal projection, Orthonormal sets, Orthonormal basis.

899 Views

Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.

832 Views

Gram-schmidt process, Orthonormal bases, Orthogonal decomposition theorem, Best approximation theorem.

813 Views

Orthogonality and Least square, Least square problem, Least square solution.

866 Views

Inner product spaces, Length, Distance and Orthogonality, Cauchy-schwarz inequality, Triangle inquality.

868 Views

Application of inner product spaces, Least square line, Weighted Least-squares.

946 Views

Matrix algebra, Vector spaces, Axioms of vector space, Spanning set theorem, basis theorem, Rank theorem, invertble matrix theorem.