267 Views

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

193 Views

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

180 Views

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

199 Views

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

115 Views

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

144 Views

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

134 Views

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

96 Views

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

96 Views

Charecterizations of invertibe matrices, Invertibe matrix theorem.

136 Views

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

109 Views

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

92 Views

Coordinate system, Graphical interpretation of coordinates.

120 Views

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

103 Views

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

104 Views

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

97 Views

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

142 Views

Eigenvalues and Eigenvectors, Fixed point, Unifying thearem.

111 Views

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

91 Views

Eigenvectors and Linear transformations, Matrix of linear transformation.

106 Views

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

88 Views

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

103 Views

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

88 Views

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

94 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.

119 Views

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

103 Views

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

106 Views

Orthogonal projection, Orthogonal decomposition theorem, Best approximation theorem.

131 Views

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

93 Views

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

94 Views

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

153 Views

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

108 Views

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