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01 Semesters (BSc)
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Semester 1
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Linear Algebra
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Lecture Notes
Folder: 01-Semesters-(BSc)/Semester-1/Linear-Algebra/Lecture-Notes
28 items under this folder.
Jan 07, 2026
01 Vectors
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02 Vectors
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03 Linear Dependence and Independence
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04 Matrices and Linear Combinations
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05 Transpose and Multiplication
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06 CR-Factorization and Linear Transformations
Jan 07, 2026
07 Linear Transformations, Linear Systems of Equations, PageRank
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08 Gauss Elimination, Elimination Matrices and Solution Sets
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09 Elementary Row Operations, Gauss Elimination, Inverse Matrices, Inverse Theorem
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10 Calculating the Inverse, LU and LUP Decomposition
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11 Gauss-Jordan, REF, RREF, Properties of REF
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12 Vector Spaces, Subspaces
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13 Vector Spaces, Bases, Dimension
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14 Fundamental Subspaces, Column Space, Row Space, Nullspace
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15 Orthogonal Vectors and Orthogonal Complements of Subspaces
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16 Orthogonal Complementary Subspaces, Projections, Normal Form
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17 Projections, Least Squares, Linear Regression
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18 Orthonormal Bases, Properties of Orthogonal Matrices
Jan 07, 2026
19 Gram-Schmidt Process, QR-Decomposition, Properties of Q and R
Jan 07, 2026
20 Pseudoinverses, Constructing Pseudoinverses
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21 Certificates, Linear Systems of Inequalities, Projections of Polyhedra, Farkas Lemma
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22 Determinants, Permutations, Properties, Cofactors, Cramers Rule
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23 Eigenvalues and Eigenvectors, Complex Numbers
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24 Explicit Fibonacci Formula, Eigenvalue and Eigenvector properties, Trace
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25 Eigenvalues, Eigenvectors, Complete Set of Eigenvectors, Diagonalization, Eigendecomposition
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26 Symmetric Matrices, Spectral Theorem, Rayleigh Quotient
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27 Positive (Semi)Definite Matrices, Gram Matrices, SVD
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28 SVD Theorem and Proof, SVD Abstraction, Pseudoinverse