Linear Algebra: A Problem Based Approach

Solving Cool Linear Algebra Problems like there is no tomorrow
What you'll 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
Requirements
A certain degree of mathematical maturity is recommended. For instance you should no some basic precalculus and know how to solve simple equations such as 2x = 3
You should be curious and willing to ask questions
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
SVD (Singular value decomposition) - In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix.

The course is highly dynamic and content is uploaded regularly.

Happy Linear Algebra !

Who this course is for:
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

More Info