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Solving Cool Linear Algebra Problems like there is no tomorrow
Updated on Sep, 2026
Teaching and Academics , Math, Linear Algebra
Duration - 16.5 hours
Training 5 or more people ?
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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 :
Linear Systems of Equations, Gaussian Elimination
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
Happy Linear Algebra!
Check out the detailed breakdown of what’s inside the course
Dr. Ron Erez has been programming for over 30 years and has always been amazed by the creativity and satisfaction of writing computer programs. Ron is also an experienced teacher having taught mathematics, computer science and English literature from middle school to university level courses.
In Ron's free time he is out cooking, cleaning, skateboarding and just living life.
I hope you enjoy taking my course as much as I enjoyed teaching it.
Good luck on your journey to learn something new and exciting.
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