Questions and comments below will be promptly addressed.

Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications.

Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually.

Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects.

This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels.

Numerous exercises will be provided via the Lemma system (under development)

We will cover the following topics:
Vectors
Linear combinations
Decomposition
Linear independence
Null space
Span
Linear systems
Gaussian elimination
Matrix multiplication and matrix algebra
The inverse of a matrix
Elementary matrices
LU decomposition
LDU decomposition
Linear transformations
Determinants
Cofactors
Eigenvalues
Eigenvectors
Eigenvalue decomposition (also known as the spectral decomposition)
Inner product (also known as the scalar product and dot product)
Self-adjoint matrices
Symmetric matrices
Positive definite matrices
Cholesky decomposition
Gram-Schmidt orthogonalization
QR decomposition
Elements of numerical linear algebra

I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the unit tangent vector T(t) of a given position vector r(t) when t=2, T(t=2)=? Next video in the series can be seen at: https://youtu.be/-eCrYgFRYXY

The basics to solving quadratic inequalities. I advocate using sketching the curve method instead of using number lines and sign test method. If you like what you see, please subscribe to this channel! http://www.youtube.com/subscription_center?add_user=numberskill For more videos, please visit http://www.numberskill.com/board-casts-on-youtube/#Bookmark Like us on Facebook http://www.facebook.com/garyang.math Follow us on Google+ https://plus.google.com/117074002101017934426/posts

Before the United States had the Constitution, it had the Articles of Confederation, a much weaker government that lasted from 1777 to 1789. In this video, Kim and Leah discuss the pros and cons of the Articles, and the reasons they were discarded in favor of a new Constitution. View more lessons or practice this…

Amazing, Life Changing Tutor
Before I met Jonathan, I was struggling through most of my STEM classes because I was simply not studying properly. He taught me all kinds of new study habits that would help me to save time, raise my grades, and lower my stress. Jonathan was specifically tutoring me in vector calculus and is an amazing tutor on the subject. You will walk away from a lesson with a game plan knowing exactly what you need to do before your next session with him or before your next exam in order to do well in the course. I highly recommend him as a tutor.