Linear Algebra: A Problem Based Approach
Solving Cool Linear Algebra Problems like there is no tomorrow
Description
The focus of this course is on solving problems. Where the best way to benefit from the course is to ask questions and in hand I will respond with answers involving exercises that expand upon the questions.
The topics covered are :
Why Linear Algebra?
Linear Systems of Equations, Gaussian Elimination
Matrices
Rank, Trace and the Determinant of a matrix. These are important invariants in Linear Algebra
Vector spaces and sub-vector spaces
Basis, dimension, linear dependence/independence, spanning sets and span
Important vector spaces : Null space of a matrix, row and column spaces of a matrix, Span of a set, intersection, sum and direct sum of vector spaces, eigenspace, orthogonal complement, Kernel and Image of a linear transformation
Linear transformations. Conditions of a linear transformation to be injective, surjective, bijective
Relation between matrices and linear transformations. Coordinates, Matrices representing a linear transformation
Dimension theorems - This is a very important and powerful topic
Eigenvalues, Eigenvectors and Diagonalization
Inner product spaces, norms, Cauchy-Schwartz, general law of cosines - An inner product space is a vector space along with an inner product on that vector space. When we say that a vector space V is an inner product space, we are also thinking that an inner product on V is lurking nearby or is obvious from the context
The course is highly dynamic and content is uploaded regularly.
Happy Linear Algebra !
What You Will Learn!
- Learn how to solve problems in linear algebra
- Grasp important and abstract concepts in linear algebra
- Understand the importance of linear algebra
- Learn how to ask interesting questions in Linear Algebra
Who Should Attend!
- You should be open to asking as many questions as possible
- This course is excellent for anyone who is preparing for an exam since the focus is on problem solving and you can always ask questions in the course
- Anyone who wants to gain a deeper understanding of Linear Algebra