NOC:Linear Algebra (Prof. Pranav Haridas)

Lecture 1 - Vector Spaces

Lecture 2 - Examples of Vector Spaces

Lecture 3 - Vector Subspaces

Lecture 4 - Linear Combinations and Span

Lecture 5 - Linear Independence

Lecture 6 - Basis

Lecture 7 - Dimension

Lecture 8 - Replacement theorem consequences

Lecture 9 - Rank Nullity

Lecture 10 - Linear Transformations

Lecture 11 - Linear Transformation Basis

Lecture 12 - Linear Transformation and Matrices

Lecture 13 - Problem session

Lecture 14 - Linear Transformation and Matrices (Continued...)

Lecture 15 - Invertible Linear Transformations

Lecture 16 - Invertible Linear Transformations and Matrices

Lecture 17 - Change of Basis

Lecture 18 - Product of Vector Spaces

Lecture 19 - Quotient Spaces

Lecture 20 - Dual Spaces

Lecture 21 - Row operations

Lecture 22 - Rank of a Matrix

Lecture 23 - Inverting matrices

Lecture 24 - Determinants

Lecture 25 - Problem Session

Lecture 26 - Diagonal Matrices

Lecture 27 - Eigenvectors and eigenvalues

Lecture 28 - Computing eigenvalues

Lecture 29 - Characteristic ploynomia

Lecture 30 - Diagonalizibility

Lecture 31 - Multiplicity of eigenvalues

Lecture 32 - Invariant subspaces

Lecture 33 - Complex Vector Spaces

Lecture 34 - Inner Product Spaces

Lecture 35 - Inner Product and Length

Lecture 36 - Orthogonality

Lecture 37 - Problem Session

Lecture 38 - Problem Session

Lecture 39 - Orthonormal Basis

Lecture 40 - Gram Schmidt Orthogonalization

Lecture 41 - Orthogonal Complements

Lecture 42 - Problem Session

Lecture 43 - Riesz Representation Theorem

Lecture 44 - Adjoint of a linear transformation

Lecture 45 - Problem Session

Lecture 46 - Normal Operators

Lecture 47 - Self Adjoint Operators

Lecture 48 - Spectral Theorem