535 Views

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

333 Views

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

314 Views

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

316 Views

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

223 Views

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

251 Views

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

227 Views

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

217 Views

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

189 Views

Charecterizations of invertibe matrices, Invertibe matrix theorem.

232 Views

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

187 Views

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

183 Views

Coordinate system, Graphical interpretation of coordinates.

209 Views

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

179 Views

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

207 Views

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

224 Views

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

220 Views

Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.

215 Views

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

197 Views

Eigenvectors and Linear transformations, Matrix of linear transformation.

196 Views

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

172 Views

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

228 Views

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

165 Views

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

177 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.

202 Views

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

195 Views

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

215 Views

Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.

196 Views

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

158 Views

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

177 Views

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

228 Views

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

188 Views

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