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Oxford Linear Algebra: Dimension Formula for Vector Spaces
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- čas přidán 22. 04. 2023
- University of Oxford mathematician Dr Tom Crawford introduces the dimension formula for vector spaces via a worked example before going through a complete proof. Check out ProPrep with a 30-day free trial to see how it can help you to improve your performance in STEM-based subjects: www.proprep.uk...
Links to the other videos mentioned:
Subspace Test - • Oxford Linear Algebra:...
Basis, Spanning and Linear Independence - • Oxford Linear Algebra:...
Test your understanding of the content covered in the video with some practice exercises courtesy of ProPrep. You can download the workbooks and solutions for free here: api.proprep.co...
You can also find several video lectures from ProPrep explaining the content covered in the video at the links below.
Dimension Formula: www.proprep.co...
Sum of Subspaces: www.proprep.co...
As with all modules on ProPrep, each set of videos contains lectures, worked examples and full solutions to all exercises.
Watch the other videos from the Oxford Linear Algebra series at the links below.
Solving Systems of Linear Equations using Elementary Row Operations (ERO’s): • Oxford Linear Algebra:...
Calculating the inverse of 2x2, 3x3 and 4x4 matrices: • Oxford Linear Algebra:...
What is the Determinant Function: • Oxford Linear Algebra:...
The Easiest Method to Calculate Determinants: • Oxford Linear Algebra:...
Eigenvalues and Eigenvectors Explained: • Oxford Linear Algebra:...
Spectral Theorem Proof: • Oxford Linear Algebra:...
Vector Space Axioms: • Oxford Linear Algebra:...
Subspace Test: • Oxford Linear Algebra:...
Basis, Spanning and Linear Independence: • Oxford Linear Algebra:...
The video begins by defining the dimension of a vector space as the number of elements in its basis. This is then exemplified by looking at the vector space of polynomials up to degree n, which has a dimension of n+1.
We then go through a fully worked example in R^4 by calculating explicitly the dimensions of the subspaces X and Y, the subspace X+Y, and the intersection of X and Y. This is used as motivation for the dimension formula: dim(X+Y) = dim(X) + dim(Y) - dim(X and Y).
Finally, a complete proof of the dimension formula is presented where we construct a basis of the space X+Y which is shown to be both spanning and linearly independent.
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac....
For more maths content check out Tom's website tomrocksmaths....
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Get your Tom Rocks Maths merchandise here:
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Check out ProPrep with a 30-day free trial to see how it can help you to improve your performance in STEM-based subjects: www.proprep.uk/info/TOM-Crawford
Hi Tom
Earlier this year, I applied for physics at Merton and was rejected. During this time I had quite bad mental health problems and my grades and tests suffered. I know I scored reasonably well (just above average) on the entrance exam, but I came out feeling disappointed, knowing that I could have done better. I was unfortunately part of the minority that was not interviewed for my score.
Recently, I’ve been wondering whether to reapply. I am finally feeling more like myself and I’m quite happy because I’ve done really well on my mocks. If I were to reapply, would I have a reasonable shot of getting in? I’ve tried to search for the admissions statistics for re-applicants but I haven’t found anything. Also I know gap years are not favoured in STEM. Any advice would be amazing.
Also just want to say I love the channel. You always have really clear and well presented content and it’s much more Mathy than other channels. Please keep up the great work :).
I must say I do love the smell of linear algebra in the morning.
Don’t we all!
Hello, I am a last year high school student in Bolivia, I am 17 years old, I decided to study mathematics permanently, but blindly because I don't know how much I like mathematics, or if I have an abstract mind for research, but still my love for math predominated despite the fact that I had already been deciding to study medicine but it was only because lately I have been losing myself in medical series and I had the illusion, in short, what depressed me about being a mathematician or even a physicist is that both sciences I feel that it has lost its essence, that is, it has been prostituted as an instrument of dissemination in order to make physics seem like child's play and mathematics like a spectacular adventure, in addition to the fact that many of their famous characters from both are so acquaintances that make you see the lives of these characters more than their work and even I have been very sympathetic with them since I value myself so little that I prefer to compare myself with people who had the same personality as me and triumph in life, so I sold myself that illusion. Another thing is that many famous mathematicians or physicists were born intelligent and gifted or else they became obsessed with matter from childhood and they investigated on their own and saw that they have talent, I have none of that, I chose study the degree as an epiphany and because if I was interested in those subjects, but I can't find a solid relationship with mathematics or physics, I can't and my worst fear is not knowing my talent or what I am suitable for, I perceive myself as someone insignificant who sometimes I think about death or the past, and as having been born in a country like Bolivia and being a student in a Catholic school in which I am an average student, even though I was recognized as the 3rd best, I am not able to assess This honor because it is from a school that I do not consider intellectually demanding or stimulating, I tried to join Cheenta's group (Indian youtube song about mathematics) but they rejected me or rather they eliminated me because at that moment I had given up being a mathematician, Now I'm looking for a mentor or tutor to help me strengthen my math skills. I hope someone cares to read this comment.
@@saifahmad141 Thank you for your support, my problem is that I'm plagued with information and I don't know how to start, that's why I'm looking for a mentor
Make a video on JEE advanced paper.....i have mine in a one and a half month...
really enjoy watching ur videos
📔📕📖📗📙📘📚📓📑
😍 I like Algebra.❤ It remembered me: Kerf (X), Img (X), canonical or orthonormal bases of X as a vectorial subspace of V.
U are absolutely good teacher dude...With gorgeous style...
Hey Dr Tom! Did you see the news that the Ukrainian high school girls mathematics team won the European Girls' Mathematical Olympiad that was just held in Slovenia? Congratulations to them!
Come-on, Tom, I am still waiting for an armwrestling between you and at least one of your maths students to be youtubed here !
Could you please do a series on what makes a good mathematician? Such things like what you taught Mike Boyd! Thank you kind sir
plz try jee adv 2022 paper
Tom could you do a video of you doing an Ib higher level aa math paper 1
grassman's theorem, poggers
👏
Grassman theorem 😲
Hii I am from India
I have not got a clue about what your taking about . But I love watching maths 🧮 videos. 😊🤣
As long as you’re having fun :)
@@TomRocksMaths i really wish I had an aptitude for maths . Unfortunately it’s not to be . However I enjoy the way you explain things . 😊👍
Challenge: JEE ADVANCED MATHS
Easyy
gonna tell my kids this was mgk
Maybe Sir Isaac Newton rocks math too! 🤘prof. ever ⚽️🔢💯 #LOL