Modules / Lectures

Sl.No Chapter Name English
11. Introduction to the Course Contents.PDF unavailable
22. Linear EquationsPDF unavailable
33a. Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations, Row-equivalent matricesPDF unavailable
43b. Equivalent Systems of Linear Equations II: Homogeneous Equations, ExamplesPDF unavailable
54. Row-reduced Echelon MatricesPDF unavailable
65. Row-reduced Echelon Matrices and Non-homogeneous EquationsPDF unavailable
76. Elementary Matrices, Homogeneous Equations and Non-homogeneous EquationsPDF unavailable
87. Invertible matrices, Homogeneous Equations Non-homogeneous EquationsPDF unavailable
98. Vector spacesPDF unavailable
109. Elementary Properties in Vector Spaces. SubspacesPDF unavailable
1110. Subspaces (continued), Spanning Sets, Linear Independence, DependencePDF unavailable
1211. Basis for a vector spacePDF unavailable
1312. Dimension of a vector spacePDF unavailable
1413. Dimensions of Sums of SubspacesPDF unavailable
1514. Linear TransformationsPDF unavailable
1615. The Null Space and the Range Space of a Linear TransformationPDF unavailable
1716. The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector SpacesPDF unavailable
1817. Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank IPDF unavailable
1918. Equality of the Row-rank and the Column-rank IIPDF unavailable
2019. The Matrix of a Linear TransformationPDF unavailable
2120. Matrix for the Composition and the Inverse. Similarity TransformationPDF unavailable
2221. Linear Functionals. The Dual Space. Dual Basis IPDF unavailable
2322. Dual Basis II. Subspace Annihilators IPDF unavailable
2423. Subspace Annihilators IIPDF unavailable
2524. The Double Dual. The Double AnnihilatorPDF unavailable
2625. The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its TransposePDF unavailable
2726. Eigenvalues and Eigenvectors of Linear OperatorsPDF unavailable
2827. Diagonalization of Linear Operators. A CharacterizationPDF unavailable
2928. The Minimal PolynomialPDF unavailable
3029. The Cayley-Hamilton TheoremPDF unavailable
3130. Invariant SubspacesPDF unavailable
3231. Triangulability, Diagonalization in Terms of the Minimal PolynomialPDF unavailable
3332. Independent Subspaces and Projection OperatorsPDF unavailable
3433. Direct Sum Decompositions and Projection Operators IPDF unavailable
3534. Direct Sum Decomposition and Projection Operators IIPDF unavailable
3635. The Primary Decomposition Theorem and Jordan DecompositionPDF unavailable
3736. Cyclic Subspaces and AnnihilatorsPDF unavailable
3837. The Cyclic Decomposition Theorem IPDF unavailable
3938. The Cyclic Decomposition Theorem II. The Rational FormPDF unavailable
4039. Inner Product SpacesPDF unavailable
4140. Norms on Vector spaces. The Gram-Schmidt Procedure IPDF unavailable
4241. The Gram-Schmidt Procedure II. The QR Decomposition. PDF unavailable
4342. Bessel's Inequality, Parseval's Indentity, Best ApproximationPDF unavailable
4443. Best Approximation: Least Squares SolutionsPDF unavailable
4544. Orthogonal Complementary Subspaces, Orthogonal ProjectionsPDF unavailable
4645. Projection Theorem. Linear FunctionalsPDF unavailable
4746. The Adjoint OperatorPDF unavailable
4847. Properties of the Adjoint Operation. Inner Product Space IsomorphismPDF unavailable
4948. Unitary OperatorsPDF unavailable
5049. Unitary operators II. Self-Adjoint Operators I.PDF unavailable
5150. Self-Adjoint Operators II - Spectral TheoremPDF unavailable
5251. Normal Operators - Spectral TheoremPDF unavailable

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