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18. Properties of Determinants
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Dterminants is my fav part of linear Algebra xD
i didn't learn anything about linear algebra at my own university. then I found these lectures from MIT.
this stuff is GOLD!!
the most interesting algebra ever. thank you professor!!
@greekman234 not if you go into the deep theory. this sucks.
just applying it is a nobrainer tho
@seisdoesmatter The chalk's really awesome. Looks thicker than ordinary chalk. It seems a bit like the chalk kids use to paint on the pavement!
These videos are amazing for test review. My linear algebra teacher is awesome but these videos are nice to watch since hopefully I already know everything going on.
u forgot to multiplay c and d with 5 in 21:10
for det( A + B ) = ? there is no formula….
wtf this math is trivial
@slatz20
he explains that if you multiply only one row. so he did it correct.
@slatz20
he explains that if you multiply only one row! so he did it correct
Property 2 wasn't needed as a fundamental property, since it follows from property 3.
my prof. can come and learn from this prof.
Same comment as everyone else. This was a much better explanation than my professor gave.
seems that i have been in this classroom before, for some information theory course.
thanks a lot, professor
I am so addicted to these lectures..
Thanks MIT and Prof Gilbert Strang.
Does anyone have a good proof for property 9?
He is really good…thx for uploading this
bu adam süper değil mi yahu
I Really Like The Video Lecture 18: Properties of Determinants From Your
thanks proffesor
We love you
Man! you are an inspiring mathematician. If i become one, full credit to you…..
Love your name.
27:30 EUREKA!
thanks!
@Bubblewhip341 lol. MIT is not an Ivy league school (although it's still a top notch college).
Only dummies will dislike this video
And for that matter: why are these comments repeated in every single lecture from the course, with the exact same wording and just the title of the lecture swapped?
just say wow.
Welcome to the world of Spam^^
This works for me. Thanks
대박!!
He is a virtuoso
thanks …
What a cute professor
"I see what you did there!" STRANGthen!
xgh
I love when he's building up to property 3. You can tell how excited he's getting (adjusting his hair, taking little pauses). Very cute
Gilbert Strang is gifted in two ways. Not only he possesses the knowledge and expertise necessary to be a math professor, but also he has the charisma that encourages people to both listen and enjoy what he is talking about.
At 45:30 he describes the "L" matrix as "Lower triangular matrix with 1s on the diagonal". In this case "L" is not exactly lower triangular but a special form of lower triangular matrix. Isn't it? Because I think the diagonal of lower triangular matrix doesn't have to consist of 1s …
It is just fantastic !!!
Thank you !!!!
Another way to prove that the determinant of a matrix with a zero row is zero would be to add one of the other rows to that row. That would create a duplicate row, which he proved the determinant of was zero.
Prof. Psaltakis is better !!!
Does anyone know which lecture he derive the general equation for a determinant? Would be a massive help thanks!
One important thing determinant says about a matrix is how much the volume/area/length is changing. Everything become much clearer with determinants when you learn this fact. There exist very good videos on Youtube about it, where you can see it in action.
can someone please explain the ending statements he made about the second property
Where do the first three properties come from?
What does 'when A is singular' mean at 29:00?
Determinant
16:00 Property 5, I think, is basically the statement that a SHEAR doesn't change the volume (or area if we're in 2D) of an object.
Just brilliant! Professor Strang teaches with so much respect for the intelligence of his students. And so many textbooks need to rewritten to establish these initial premises (properties) of determinants. (Teaching, learning and importantly understanding math is a NOT a recipe process, rather derived and built from simple premises.)
This is the best introduction to determinants, that I have seen so far.
I AM COMING TO YOU TO LEARN MATHEMATICS FROM BASICS.
can anyone share how we get property 9 from the properties 13 ?
I can see why American people are by far well educated .
HAT OFF TO YOU
Thanks to you we really start to see what s going on in Algebra
God I love him.
33:36 "That's what she said."
Determinant has been determined. Thank you MIT!
best det class i ever had.
While in high school (in India), I used to hate matrices, determinants, and vectors. They taught it like they were just a bunch of mindless, random calculations. Prof. Strang gives meaning to all of them and linear algebra has suddenly become wayyyy more interesting!
40:57 hes def sniffing smt
The GOAT
I was 9 years old when this video was recorded. lol
800th upvote. Very good video!
Closing comment was confusing. What did he mean by permutations can either be odd or even?
The definition is just brilliant
this is brilliant, why did i ever bother attending live lectures at my university
Thank you.
https://youtu.be/srxexLishgY?list=PLE7DDD91010BC51F8&t=858
Oh, ohh, ohhh. There was a party before and now all the bottles are empty.
~22:10 "now I have to get serious"
so, what was all that other stuff?
Lecture 18: Properties of determinants
Lecture 19: Determinant formulas and cofactors
Lecture 20: Cramer's rule, inverse matrix, and volume
Lecture 21: Eigenvalues and eigenvectors
Lecture 22: Diagonalization and powers of A
Lecture 23: Differential equations and exp(At)
Lecture 24: Markov matrices; fourier series
Lecture 24b: Quiz 2 review
Lecture 25: Symmetric matrices and positive definiteness
Lecture 26: Complex matrices; fast fourier transform
Lecture 27: Positive definite matrices and minima
Lecture 28: Similar matrices and jordan form
Lecture 29: Singular value decomposition
Lecture 30: Linear transformations and their matrices
Lecture 31: Change of basis; image compression
Lecture 32: Quiz 3 review
Lecture 33: Left and right inverses; pseudoinverse
Lecture 34: Final course review
0:50 Start : Determinant
2:30 Three properties of determinant
5:29 Formula and third property
11:47 Property four
14:31 Property five
– 16:35 2×2 matrix
19:06 Property six
22:12 property seven and eight
33:41 Property nine
41:37 Property ten
– 43:44 Proof
– 45:29 Practice
Free education X D
at 27:00, how come you are just able to factor out the diagonals? If you take out d1, arent all the diagonals in the matrix from the 2nd row to the nth row, dn/d1?
The way he says "Kill" makes him sound serious @ 25:56
wow ! That's Beautiful !!!
Love you Professor. You are such an adorable person and a great great teacher!
Greetings from New York City!
Prof. Strang was my Linear Algebra 18.700 professor during my sophomore year at MIT in Spring 1973. I loved his teaching style, did well on the tests, and received an “A” in the class.
Did we prove det(AB) = detA*detB in the lecture?
Fantastic lecture!
Thank you Professor Strang.
thanks
very informative, thanks.
For property 3b should the top row be (a+a' b) –> (a b) + (a' b)
40:30 The 3B1B perspective of areas and volumes for determinants.
Does anyone know which lecture did Prof. Strang talk about singular matrix?
Must watchhttps://youtu.be/lVUVWdECVVM