Modules / Lectures
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Sl.No Chapter Name English
1Introduction to the CourseDownload
Verified
2Vector Spaces: IntroductionDownload
Verified
3Linear Combinations and SpanDownload
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4Subspaces, Linear Dependence and IndependenceDownload
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5Basis and DimensionDownload
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6Sums, Direct Sums and Gaussian EliminationDownload
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7Linear Maps and MatricesDownload
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8Null space, Range, Fundamental theorem of linear mapsDownload
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9Column space, null space and rank of a matrixDownload
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10Algebraic operations on linear mapsDownload
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11Invertible maps, Isomorphism, OperatorsDownload
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12Solving Linear EquationsDownload
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13Elementary Row OperationsDownload
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14Translates of a subspace, Quotient SpacesDownload
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15Row space and rank of a matrixDownload
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16DeterminantsDownload
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17Coordinates and linear maps under a change of basisDownload
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18Simplifying matrices of linear maps by choice of basisDownload
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19Polynomials and RootsDownload
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20Invariant subspaces, Eigenvalues, EigenvectorsDownload
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21More on Eigenvalues, Eigenvectors, DiagonalizationDownload
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22Eigenvalues, Eigenvectors and Upper TriangularizationDownload
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23Properties of EigenvaluesDownload
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24Linear state space equations and system stabilityDownload
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25Discrete-time Linear Systems and Discrete Fourier TransformsDownload
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26Sequences and counting paths in graphsDownload
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27PageRank AlgorithmDownload
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28Dot product and length in Cn, Inner product and norm in V over FDownload
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29Orthonormal basis and Gram-Schmidt orthogonalisationDownload
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30Linear Functionals, Orthogonal ComplementsDownload
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31Orthogonal ProjectionDownload
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32Projection and distance from a subspaceDownload
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33Linear equations, Least squares solutions and Linear regressionDownload
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34Minimum Mean Squared Error EstimationDownload
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35Adjoint of a linear mapDownload
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36Properties of Adjoint of a Linear MapDownload
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37Adjoint of an Operator and Operator-Adjoint ProductDownload
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38Self-adjoint OperatorDownload
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39Normal OperatorsDownload
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40Complex Spectral TheoremDownload
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41Real Spectral TheoremDownload
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42Positive OperatorsDownload
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43Quadratic Forms, Matrix Norms and OptimizationDownload
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44IsometriesDownload
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45Classification of OperatorsDownload
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46Singular Values and Vectors of a Linear MapDownload
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47Singular Value DecompositionDownload
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48Polar decomposition and some applications of SVDDownload
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Sl.No Language Book link
1EnglishNot Available
2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
8TamilNot Available
9TeluguNot Available