The Gram-Schmidt process | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/line...
Finding an orthonormal basis for a subspace using the Gram-Schmidt Process
Watch the next lesson: www.khanacademy.org/math/line...
Missed the previous lesson?
www.khanacademy.org/math/line...
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: / channel
Subscribe to KhanAcademy: kzread.info_...
Пікірлер: 121
For me, 20 minutes of this is worth more than a 2 hour lecture. Thank you!
Khan Academy coming in clutch right before my Linear Algebra final
Although my linear algebra instructor made this easy to follow in terms of the steps and calculations, watching this video I know actually understand WHAT we are doing when we perform these steps. Thank you Sal for the great video tutorial.
Saving mathematic lives out here, thanks fam
I am so confused.
damn your U :p
This felt so intuitive... my mind is blown. Thank you for showing us why math is so cool!
A day before my optional resit of quantum mechanics and here Khan Academy is, saving the day again.
I don't have words to show how grateful I feel now
Hes definitely right when he said its not that bad when youre dealing with the numbers. Memorize the equations and its not too bad. Understanding the proof and why is the hard part.
i've never understood this quite right at college but now as i take only this one 20 minute lecture at khanacademy i understand everything. thank you!!
That awkward moment when you understand something in maths :') Thanksss!!
Thank you so much, i am so grateful to you Sal. You literally changed everything....
This is so well explained. I had to go back watch it twice though. But makes complete sense now. Thank you so much!!!!
You're truly great at teaching! Thanks and good luck!
Man this guy's the best. Been using these vids since middle school, and I'm in grad school now. Thanks Khan Academy
thank you khan academy ,it was really useful .i was struggling to understand hilbert space now you made it easy.
It became clear later on in the video. thank you so much for making it free!
Thanks kahn. You're really helpin me out with my math classes
great sir!! i love listening to your way of explaining things