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

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

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

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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34 Responses to “Surjective (onto) and injective (one-to-one) functions | Linear Algebra | Khan Academy”

  1. Python Cure says:


  2. Blasted Shark says:

    That guy who never gets mapped to is me

  3. Zeina Ayman says:

    These comments make me feel young

  4. Priyams Bajracharya says:

    Anyone in 2021?

  5. shreya bayari says:

    on point and short. Loved it!

  6. Alperen Hyper says:

    saolun hocam

  7. ab says:

    midterms tomorrow thanks for this ^^

  8. shu says:

    why does sal have such a beautiful voice

  9. Jigyasa Chopra says:

    Thank u sir! Well explained ❤️

  10. chemical bank says:

    what does it mean * mapping from the x set to y set* and also f of x is equal to y

  11. Jennifer says:

    i'm taking online discrete math course rn due to covid, prof posted lecture, but couldn't understand any. Thank you for posting videos abt this.

  12. Aadharsh Balasaravanan says:

    We can't get videos like this even one of the paid applications that u would have.

  13. Aadharsh Balasaravanan says:

    Great person.

  14. FRANXIS says:

    Still can't conceive how the people in these maths videos can write using a mouse like it was a pen

  15. Samurai7 says:

    Explained very clearly

  16. Harsh Kumar says:

    Bio students: that's Amoeba😂

  17. stephen awuah says:

    I have a question
    How do u know that the codomain is the same as the range

  18. stephen awuah says:

    I have a question
    How do u know that the codomain is the same as the range

  19. s sanjay says:

    This 9 min video= 2 hour lecture

  20. Arshad says:


  21. CryoniX says:

    I thought Injective (ie not Surjective) meant that Y can't have many X. From what I know, what you are describing at 3:55 is a general function.

  22. Raj Kumar says:

    Woah it's 11 years now!!

  23. BE LOGICAL says:

    will someone plz tell me how can two differnt values of x give same answer in a function? i mean how can4 and 5 both map to D

  24. 7ANKOUCH says:

    Thank youuuuuu my I undrestand now

  25. BrittBratt3000 says:

    So the image = range?

  26. Luka Zec says:

    Gosh thx Khan academy! Amazing and easy way of explaining just what I needed to get back on track

  27. Deatrix says:

    but how do i translate this from a more complex problem? what if f : x —> x and f(x)=3x and x are real numbers? is there a video that addresses this sort of problem?

  28. chinmay bhat says:

    Dear Sir,
    Why the Video Audio is not supporting in Google chrome ?? Kindly guide me in this issue

    Thanks & Regards,


    What if one of the x elements is not associated to any y elements? Is it a function or not?

  30. Erick Cabrera says:


  31. J P says:

    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.

  32. sreelekshmi ms says:

    Thank you 👏

  33. Shuvo Sarker says:

    Watching Khan's videos are like eating raspberry pie or like listening poetry.

  34. Fahad says:

    Amazing explanation thank you.

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