1734 Views

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

1067 Views

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

956 Views

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

1082 Views

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

839 Views

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

914 Views

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

850 Views

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

914 Views

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

858 Views

Charecterizations of invertibe matrices, Invertibe matrix theorem.

865 Views

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

887 Views

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

1073 Views

Coordinate system, Graphical interpretation of coordinates.

892 Views

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

728 Views

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

812 Views

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

803 Views

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

970 Views

Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.

838 Views

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

756 Views

Eigenvectors and Linear transformations, Matrix of linear transformation.

756 Views

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

906 Views

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

834 Views

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

717 Views

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

670 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.

814 Views

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

740 Views

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

773 Views

Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.

676 Views

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

688 Views

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

746 Views

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

747 Views

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

743 Views

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