1414 Views

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

768 Views

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

706 Views

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

816 Views

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

610 Views

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

621 Views

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

603 Views

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

650 Views

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

568 Views

Charecterizations of invertibe matrices, Invertibe matrix theorem.

562 Views

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

599 Views

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

687 Views

Coordinate system, Graphical interpretation of coordinates.

584 Views

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

497 Views

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

569 Views

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

580 Views

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

689 Views

Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.

570 Views

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

529 Views

Eigenvectors and Linear transformations, Matrix of linear transformation.

484 Views

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

588 Views

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

564 Views

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

487 Views

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

456 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.

556 Views

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

533 Views

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

538 Views

Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.

469 Views

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

463 Views

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

528 Views

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

527 Views

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

506 Views

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