Lecture 15 of 49Week 4
Invertible Linear Transformations
Prof. Pranav Haridas · Kerala School of Mathematics
Credits and licence
- From
- Linear Algebra, Kerala School of Mathematics (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Vector Spaces
- Examples of Vector Spaces
- Vector Subspaces
- Linear Combinations and Span
- Linear Independence
- Basis
- Dimension
- Replacement theorem consequences
- Rank Nullity
- Linear Transformations
- Linear Transformation Basis
- Linear Transformation and Matrices
- Problem session
- Linear Transformation and Matrices continued
- Invertible Linear Transformations
- Invertible Linear Transformations and Matrices
- Change of Basis
- Product of Vector Spaces
- Quotient Spaces
- Dual Spaces
- Row operations
- Rank of a Matrix
- Inverting matrices
- Determinants
- Problem Session
- Diagonal Matrices
- Eigenvectors and eigenvalues
- Computing eigenvalues
- Characteristic ploynomia
- Diagonalizibility
- Multiplicity of eigenvalues
- Invariant subspaces
- Complex Vector Spaces
- Inner Product Spaces
- Inner Product and Length
- Orthogonality
- Problem Session
- Problem Session
- Orthonormal Basis
- Gram Schmidt Orthogonalization
- Orthogonal Complements
- Problem Session
- Riesz Representation Theorem
- Adjoint of a linear transformation
- Properties of the adjoint
- Problem Session
- Normal Operators
- Self Adjoint Operators
- Spectral Theorem