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Lecture 6: Column Space and Nullspace.
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MIT 18.06 Linear Algebra, Spring 2005
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Instructor: Gilbert Strang



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Lecture 7: Solving Ax = 0: Pivot Variables, Special Solutions.
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Lecture 8: Solving Ax = b: Row Reduced Form R.
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Course Introduction
Instructor: Gilbert Strang
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Professor Gil Strang describes the key concepts of undergraduate course Linear Algebra, who should take it, and how it is taught. He provides examples of applications of linear algebra and how it is useful in physics, economics and social sciences, natural sciences, and engineering.

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Mathematician Gilbert Strang on differential equations, history of finite elements, and problems of the method.

Geometry of Linear Algebra
Instructor: Linan Chen
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Matrix multiplication and linear algebra explained with 3D animations.

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
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Instructor: Gilbert Strang

A matrix produces four subspaces: column space, row space (same dimension), the space of vectors perpendicular to all rows (the nullspace), and the space of vectors perpendicular to all columns.

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Margot Gerritsen (Stanford Computational Math) on Linear Algebra: the incredible beauty of a branch of math with a bad reputation at a USF LASER - with special thanks to Tim Davis and his beautiful matrix collection (see )

On May 16, 2011, Professor of Physics Emeritus Walter Lewin returned to MIT lecture hall 26-100 for a physics talk and book signing, complete with some of his most famous physics demonstrations to celebrate the publication of his new book For The Love Of Physics: From the End of the Rainbow to the Edge of Time - A Journey Through the Wonders of Physics, written with Warren Goldstein.

Note: Due to a serious complaint against Dr. Lewin, MIT has revoked Dr. Lewin's title of Professor Emeritus as of December 2014.
See and

This video was formerly hosted on the YouTube channel MIT OpenCourseWare.

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This YouTube channel is independently operated. It is neither affiliated with nor endorsed by the Massachusetts Institute of Technology, MIT OpenCourseWare, or Dr. Lewin.

Lecture 9: Independence, Basis, and Dimension.
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MIT tour of impressive buildings and 168 acre campus spanning over a mile along the Charles River in Cambridge, MA

Part III: Linear Algebra, Lecture 1: Vector Spaces
Instructor: Herbert Gross
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Lewin's physics lectures at MIT are legendary. What does he think about bad professors? This is what he told us in an interview at Barcelona (Spain), Feb 15. More info:

Understanding linear combinations and spans of vectors

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

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Some advice from a junior at MIT on how to maximize your odds at getting admitted.

How to Graduate from MIT:

A visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis.

Watch the full Essence of linear algebra playlist here:

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist:

Various social media stuffs:
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Lecture 10: The Four Fundamental Subspaces.
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Review sessions given at Princeton University in Spring 2008 by Adrian Banner.

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Solving Ax=b
Instructor: Martina Balagovic
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Introduction to linear subspaces of Rn

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel::
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Lecture Series on Quantum Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit

Lecture 16: Differential equations, separation of variables

*Note: this video was revised, raising the video brightness.

Lecture 17 is Exam 2, so no video was recorded.

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Swami Mukundananda was at the Massachusetts Institute of Technology (MIT) on October 12th, 2011 to deliver an enlightening talk on the topic of Technology for Mind Management. The lecture was followed by Q/A session.

He brings alive ancient truths and wisdom from the Vedic scriptures; synthesizing them with modern thought and scientific theories. His logic, wit, humor, and profound message have brought a sense of clarity and purpose to countless souls.

How to raise our life to sublime heights. Technology that we learn helps us harness the forces of external nature for the comforts of our body. However the experience of fulflilment, happiness and satisfaction does not depend on the external factors but the state of our mind. Listen to thefull lecture to know your whys and hows:

About Swami Mukundananda

Swamiji is a renowned spiritual leader, philosopher, visionary, author, and humanitarian. He is the founder of the yogic system called “JKYog.” Swamiji is a unique sanyasi (in the renounced order of life), with distinguished degrees in Engineering and Management from two world famous Institutes in India, IIT and IIM. He is the senior disciple of Jagadguru Shree Kripaluji Maharaj. Swami Mukundananda has enlightened and guided thousands of seekers on the path of God-realization with his unique blend of ancient vedic wisdom presented with a scientific and modern touch.

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swamimukundananda.org

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Art of Mind Management Part1 - Swami Mukundananda - How to control your mind?


Patanjali Yoga Sutras By Swami Mukundananda


Bhagavad Gita Chapter 12 by Swami Mukundananda in hindi



Bhagavad Gita in English [1/17] Chapter 7 - Swami Mukundananda



Bhagavad Gita in English [1/17] Chapter 7 - Swami Mukundananda

October 23, 2010 - Professor Margot Gerritsen illustrates how mathematics and computer modeling influence the design of modern airplanes, yachts, trucks and cars. This lecture is offered as part of the Classes Without Quizzes series at Stanford's 2010 Reunion Homecoming.

Margot Gerritsen, PhD, is an Associate Professor of Energy Resources Engineering, with expertise in mathematical and computational modeling of energy and fluid flow processes. She teaches courses in energy and the environment, computational mathematics and computing at Stanford University.

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This film about the matrix singular value decomposition was made in 1976 at the Los Alamos National Laboratory. Today the SVD is widely used in scientific and engineering computation, but in 1976 the SVD was relatively unknown. A practical algorithm for its computation had been developed only a few years earlier and the LINPACK project was in the early stages of its implementation. The 3-D computer graphics involved hidden line computations. The computer output was 16mm celluloid film.
--- Cleve Moler
December 4, 2012

Instructor: Prof. David Jerison
Derivatives of products, quotients, sine, cosine
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Lecture 30: Linear Transformations and Their Matrices.
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The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.
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[Free Webinar] 10 Secrets To Raise Your Child’s SAT Score & Get Into An Elite College by Perfect SAT Scorer. Register Here:

MIT 8.01 Classical Mechanics, Fall 2016
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Instructor: Prof. Deepto Chakrabarty



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Dr. Sutcliffe explains how to determine whether or not a given subset of a vector space is a subspace.

MIT developed a robot modeled after a cheetah. It can run up to speeds of 10 mph, though researchers estimate it will eventually reach 30 mph.

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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. *Please note that Lecture 4 is unavailable in a higher quality format.

Creative Commons Attribution-NonCommercial-ShareAlike 3.0;

Part I: Complex Variables, Lecture 1: The Complex Numbers
Instructor: Herbert Gross
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Lecture 1: The Geometry of Linear Equations.
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This video provides a basic outline for how we will go about studying linear algebra by attempting to answer the question: What is Linear Algebra?

Sources: The example of a linear system, as well as the terms 'row picture' and 'column picture,' are taken from Gilbert Strang's Introduction to Linear Algebra text and supplemental materials.

MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010
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Instructor: John Tsitsiklis

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Properties of Determinants
Instructor: Ana Rita Pires
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Limits, continuity; Trigonometric limits
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Lecture 1: Dot product.
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Difference Methods for Ordinary Differential Equations
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Lecture 2: Elimination with Matrices.
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MIT 8.01 Classical Mechanics, Fall 2016
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Instructor: Prof. Anna Frebel



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Lecture 3: Multiplication and Inverse Matrices.
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Derivatives, slope, velocity, rate of change
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On 7 December 2005, Mark Zuckerberg joined CS50 for a guest lecture about Facebook and computer science. With Professor Michael D. Smith. Shared with permission. CS50.tv.