Learn · Algebra 1: Foundations
Lecture 34 of 45Week 9
Spans and linear independence
Prof. Jaikrishnan J · IIT Palakkad
Credits and licence
- From
- Algebra 1: Foundations, IIT Palakkad (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
- The nature of pure mathematics
- Basic set theory
- Basic logic
- Proofs
- More about proofs
- Set theoretic identities
- Functions
- Equivalence relations
- Quotients
- More functions
- Binary operations
- Groups
- Rings and integral domains
- Peeking under the carpet
- The Integers
- Induction
- Applications of Induction.
- Uniqueness of Integers.
- Cardinality of sets
- Division in the Integers
- Congruences
- Basic number theory
- Fields
- Real numbers
- Complex numbers
- Polynomials
- System of Linear Equations
- Gaussian elimination
- Matrix Algebra
- Square systems.
- The set of solutions
- Vector spaces
- Direct sums of subspaces
- Spans and linear independence
- Basis
- Linear Maps
- The Rank--Nullity theorem
- Matrices and Linear transformations
- Change of basis
- Eigenvalues
- Minimal Polynomial
- Applications of the minimal polynomial
- Triangular Form
- Jordan Form
- Examples of Canonical Forms