Linear algebra from zero to mastery
Systems, Matrices, Vector Spaces, Linear Maps, Determinants, Diagonalization, Orthogonality and more.
Ratings 4.54 / 5.00
What You Will Learn!
- Linear system: Gaussan ellimination, system whith parameter. solve geometrically.
- Matrix: sum, multiplication, inverse, power, transpose, trace, matrix equation.
- Vector space, subspace, direct sum of subspaces, linear combination, span, linearly independent,
- Finite dimensional vector space, basis, dinension, reduce a list of vector, extend
- Linear map, compose, endomorphism, isomorphism, automorphism, kernel, image, rank, nullity-rank teheorem,
- Matrix of linear map, matrix of vector, change of bases
- matrix as linear map
- Determinant,
- Eigenvectors, eigenvalues, diagonalization, tringularization,
- Scalar product, orthoghonal projection, distance,
- Spectral theorem: orhogonal matrix, symmetric matrix and endomorphism
Description
By the end of this course,
You will be able to understand the new concepts of linear algebra step by step.
You will be able to solve by yourself the majority of the standard and many original questions,
You will be able to solve by yourself the majority of hard problems , that you will encounter in your exams or in your professional life.
You will be able to code linear algebra and solve in python.
you will be able to apply linear algebra in geometry and so on.
This course is extremely useful for students, professional and new instructors.
Why Linear algebra?
Linear algebra is a great opportunity to find a prestigious job in the future.
Linear algebra is the most used math branch by engineers, economists, biologist, data scientists, computer scientists...
This is to make data in matrix,
This is to design, analyze and solve complex systems,
This is to solve geometry and distance problems,
This is to understand how algorithms work.
Linear algebra is the branch of mathematics most used by mathematicians:
in differential calculus, analysis, probability, statistics, machine learning, graph theory and linear programming.
What is the structure of this course?
I have divided this course into many sessions.
Each session divided into short video lecture.
Followed by methods and warm-up with detailed solutions in pdf file.
Other exercises will come.
MCQ, true or false, quiz, hard problem,
geometric visualization and codes in python and other applications will be in this course.
Each video answers a question How to do just one new thing?
to clarify the difficult concepts of linear algebra.
and gives a clear strategy for solving the classic and usual problems needed in worldwide, linear algebra courses.
this course is open to your questions, and I would be very happy to answer your questions in the forum where I strongly encourage mutual aid.
What are the key parts of this course?
the key parts of this course are the videos and the warm up.
The reason I called it warm up,
is because any new job requires preparation.
It is like a game in machine or a sport in real life.
methods and new concepts must be fluid
and enters your mind like water.
it's like a baby's first steps, where your parents hold your hands to teach you to walk, how to speak simple words like mama, dadda.
is to introduce new concepts step by step with easy problems.
those problems that help you practice this topic and understand how it works with fluency.
The video lectures, methods and warm-up are to answer the famous questions:
How to do linear algebra?
And to understand new concepts step by step with fluency.
You should definitely take a look at everything in there. even if you see it very simple.
and if you see a difficult thing, you have to repeat it again and again, because this part of the course is the basis of all linear algebra and we cannot advance in the course if we don’t dominate it.
Why so many problems?
And then you get MCQ, true or false, quiz, hard problem, long problem…
That mix everything together. You walk, run and say nice understandable phrases.
by doing a lot of problems, you will improve your recognition skills, so a big part of this course is about pattern recognition.
and that just takes practice. you must practice as much as you can.
So, the more practice problems, you do the better.
Why hard problems?
Doing hard problems is like the formation of world champions in sports.
is like the work of a great jeweler who creates the royal jewels, it's the professionalism.
it is to improve thinking and reasoning skills.
But if you cannot do a hard problem, you can take a look on the solution, then redo the problem again and again until you have mastered it.
Don't forget it's a practice.
you have to know the known, to look for the unknown.
How to overcome linear algebra difficulties?
The best way to learn this course to find the solution for these warm up problems by yourself, you can also consider this as a kind of example and firsts steps to apply the methods and strategy.
then make more problems as you can or as you need.
This course is under construction.
So, every week something new.
I will be very happy to receive your encouragement and your questions.
This is for the jobs of tomorrow.
This is to form great minds of tomorrow.
Who Should Attend!
- Students engineers, bioligists, economists, data scientists, computer scientists ...
- New instructors
- All hwo like understand linear algebra methods and strategies step by step from easy to hard problems
