Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy
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Understanding the definition of a basis of a subspace Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/vector-dot-product-and-vector-length?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/subspace_basis/v/linear-subspaces?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra 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:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Comments
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يارايت يبقى فيه شرح بالعربى 😥😥
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Thanks a ton from the bottom of my heart to make such amazing and outstanding videos.
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Question: If the set S is not linearly independent, you can still have a span V of it but it is not a basis, but if the set S is linearly independent, then the span of that particular set S is a subspace of V and it is a basis?
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where is that last video please =D ??
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Thank you Sal:)! If only professors could explain and teach as you do. Again thank you so much for all the video
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his voice <3
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So, by the logic of basis, the Planck's constant is also kind of a basis for all of the possible energies that can exist. "h" spans all possible energy levels and it is independent because one can't have half the energy of a photon. I guess.
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I'm a lazy to research something about Basis or anything about that but I think if I will watch your all lessons I will be lazy as always because everything is about linear algebra is in your channel. This is enough for me to do not any research about anything. Just click your channel and enjoy :D Thanks a lot!
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Based khan academy! Finally understand this, not the abstract definition but actual examples and explanations :) If I only found you before my mid terms :(
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You are such a phenomenal teacher sal. You explain things more clearly than most college professors. Linear algebra is considered abstract to us undergrads, which it is, but you illustrate things so clearly. It reminds one that mathematics is rooted in logical reasoning and natural deduction. The way you explain things, everything is logical. So thank you very much for these videos.
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Thanks for this! I really needed a refresher!
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Check up on Out One of My Vids
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i don't even know
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You said a subspace is any set of vector in the first 30 sec but then you said they have to be linearly independent, so which one is it ?
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You the real MVP
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Why does he always assume ill remember stuff from "physics class" I never did anything like this in "physics class"!!
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"mimimu"
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At 12:05 he shows that the vectors [0,1] & [1,0] can never be scalar multiples of each other.
What about if you add them together and take some scalar multiple? -
great video to jog my memory :) thanks.
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This is awesome, I'd be screwed w/o this video
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