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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.
Dec 15, 2025
01 Vectors
Dec 15, 2025
02 Vectors
Dec 15, 2025
03 Linear Dependence and Independence
Dec 15, 2025
04 Matrices and Linear Combinations
Dec 15, 2025
05 Transpose and Multiplication
Dec 15, 2025
06 CR-Factorization and Linear Transformations
Dec 15, 2025
07 Linear Transformations, Linear Systems of Equations, PageRank
Dec 15, 2025
08 Gauss Elimination, Elimination Matrices and Solution Sets
Dec 15, 2025
09 Elementary Row Operations, Gauss Elimination, Inverse Matrices, Inverse Theorem
Dec 15, 2025
10 Calculating the Inverse, LU and LUP Decomposition
Dec 15, 2025
11 Gauss-Jordan, REF, RREF, Properties of REF
Dec 15, 2025
12 Vector Spaces, Subspaces
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13 Vector Spaces, Bases, Dimension
Dec 15, 2025
14 Fundamental Subspaces, Column Space, Row Space, Nullspace
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15 Orthogonal Vectors and Orthogonal Complements of Subspaces
Dec 15, 2025
16 Orthogonal Complementary Subspaces, Projections, Normal Form
Dec 15, 2025
17 Projections, Least Squares, Linear Regression
Dec 15, 2025
18 Orthonormal Bases, Properties of Orthogonal Matrices
Dec 15, 2025
19 Gram-Schmidt Process, QR-Decomposition, Properties of Q and R
Dec 15, 2025
20 Pseudoinverses, Constructing Pseudoinverses
Dec 15, 2025
21 Certificates, Linear Systems of Inequalities, Projections of Polyhedra, Farkas Lemma
Dec 15, 2025
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
Dec 15, 2025
25 Eigenvalues, Eigenvectors, Complete Set of Eigenvectors, Diagonalization, Eigendecomposition
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26 Symmetric Matrices, Spectral Theorem, Rayleigh Quotient
Dec 15, 2025
27 Positive (Semi)Definite Matrices, Gram Matrices, SVD
Dec 15, 2025
28 SVD Theorem and Proof, SVD Abstraction, Pseudoinverse