782 Views

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

424 Views

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

404 Views

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

441 Views

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

335 Views

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

336 Views

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

329 Views

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

313 Views

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

294 Views

Charecterizations of invertibe matrices, Invertibe matrix theorem.

315 Views

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

265 Views

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

283 Views

Coordinate system, Graphical interpretation of coordinates.

289 Views

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

241 Views

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

278 Views

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

319 Views

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

298 Views

Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.

295 Views

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

261 Views

Eigenvectors and Linear transformations, Matrix of linear transformation.

241 Views

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

246 Views

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

305 Views

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

222 Views

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

223 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.

298 Views

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

278 Views

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

298 Views

Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.

241 Views

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

209 Views

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

236 Views

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

288 Views

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

266 Views

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