Surjective (onto) and injective (one-to-one) functions | Linear Algebra | Khan Academy

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Introduction to surjective and injective functions

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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.

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For anyone watching; a term that can be used to describe a function that is both injective(one to one) and surjective(onto) is referred to as BIJECTIVE

mahmoudnadi
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this 10 min video > 2 hour lecture

thank you Sal

plaxen
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dumb f**king textbooks twists the words and sentences so hard that sometimes it is so hard to learn the material (especially theorems and definitions). Thank you Sal for making these videos.

larrypark
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My teacher made this way harder than it actually is. Thank you!

mauriciobeithia
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A minute of silence for that guy who never gets mapped to

plamenpetrov
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Sal is one of the greatest humans who have ever lived and breathed.

gaurav.raj.mishra
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rewatch it in a few minutes. should be available in hi-def then

khanacademy
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You sir are responsible for my A+, I got yesterday!
It was the only concept that wasn't clear even though my Teacher asked me about _"Do I make myself clear, "_ but I'm a shy kind so I affirmed and never got the actual concept!

raz
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This was uploaded when i wasn't even born now its here saving me in my exams.Sal saving generations

ebayaankabir
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Stop scrolling down go back to studying

artmasterpl
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This lesson is very well explained. Bravo. I couldn't understand the subject reading the textbook but now I can.

dominykasraila
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Amazing. I was sick during the explanation of this at my school and altough english is not my main tongue, this thing made it clear to me. Thanks A LOT.

mihurcina
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Thank you so I never actually understood the concept to this day. I read all the definitions at least hundred of times and still didn't get it. Watched your video for 10 minutes and finally undersood something that I didn't get in years and years of math! Really, THANK YOU SO MUCH!!

jasminemmohsin
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Your videos are the best! I wish you could be my personal tutor, I would understand everything so much better!

honeybadger
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you're just an excellent techar, why can we have a teacher like you? I was in the lecture room for 2 hrs trying to understand, but I learnt it here in 10 mins, amazing!!!

jenish
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from morocco i want to thak you for this clear explanation :))

jjknow
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You spend 3:40 just to say surjective means that every possible output of an algebraic expression must have at least one input.

TheFlemishNut
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Wow, this explanation was so clear, much better than my prof. just talking to himself on the board. You are indeed a true saint, making knowledge accessible to everybody.

JP-xmqf
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Me watching it like 13 years after its upload woah 😂

yunakim
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You might be the reason I pass Discrete math, I thank you time and time again for all your videos to reference.

InFamousStickFigure