7: Power Method for Eigenvalues - Learning Linear Algebra

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[matthewholmes]

You are a legit lifesaver, anyone got recommendations of channels as good?

[pablorc]

5:22 is where it clicked for me. Thank you very much

[archianosohliya]

I love the thumbnail as much as I love the explanation

[laneellisor]

Love your channel! Keep up the great work

[lazergurka-smerlin]

Thank you! This brought a lot of clarity to the method. I could find myself guessing how it worked halfway through so yea, I enjoy actually understanding the programming methods I am to use lol

[adrenochromeaddict]

you're actually a good teacher I regret that I avoided your video because of the anime character

[Lakesaltwalker]

Yes; this guy is good. So easy to understand

[ishaaq]

Bro!!Have a blast..Can't express my Understanding..Hats off🔥

[mertcihangiroglu]

at [07:22] you say the biggest number is 3 it is 6 obviously just wanted to mention that. Thanks for the video very clearly explained. Do you have any videos related to Lagrange interpolation or Pagerank algorithm?

[VibingMath]

Great video with funny thumbnail from dragonball 😂 A lot of power gained!

[PyroEscapeVehicle]

Brilliant video!!! Thank you for the help : )

[mayfu]

Thank you so much!!! Clearly explained!!!

[bergamobobson]

Great explanation, u have the gift to teach
But at 5:27 I think u want to say they will keep decreasing because they are actually less than 1

[zahraakhalife]

Thanks a lot🙂🙂 Why don't we raise the largest eigenvalue to the power (1/k) so that we evaluate lamda_1 ?

[holyshit]

Can you record something on QR method
but from programmer's not from mathematician's perspective
What I mean from programmer's perspective
We don't need to construct Householder matrices and multiply them in standard way
We dont need to construct Givens rotation matrices and multiply them in standard way
We can multiply matrix by Householder matrix using only O(n^2) time and O(n) space
We can multiply matrix by Givens matrix using only O(n) time and O(1) space
Mathematicians dont care about it but programmers do
Moreover I havent seen correct choice of shift so far
I would like to see how to program block QR method (we work on chosen block of the matrix instead of whole matrix)

I found how to reduce matrix to Hessenberg form via Gaussian elimination
and i write how multiplication by rotation matrices looks like
We need multiplication by rotation matrices from the left to get matrix R from matrix A
We need multiplication by rotation matrices from the right to get matrix Q from matrix I

[nenadilic]

Aren't we multiplying vector x over and over again by A? From what you said about scaling in between matrix-vector multiplications it implies multiplying the scaled right-hand side vector by A (instead of x) in the next iteration and so on, which will totally screw up the equation.

[bombster]

you missed that the initial vector cannot be an eigenvector! Otherwise the matrix will just scale out that vector and you wont get the vector associated with the dominant eigenvalue!

[holyshit]

Eigenvalues are more complicated to calculate then you presented in this video
1. We reduce matrix to Hessenberg form via transformations which preserve similarity of the matrix
(Reduction will accelerate QR decomposition of the matrix)
2. QR decomposition via reflections or rotations
3. QR method should work on the chosen block of the matrix instead on whole of the matrix
4. We should choose shift properly which isnt explain well
In fact multiplication by reflection matrices and by rotation matrices also isnt explained well

[rob]

Great video. We never learnt this method way back when. I suppose this is because it is fairly inconvenient to apply if you don't have a tool like Excel. With Excel, it becomes a fairly simple task. Is it possible to use some kind of extrapolation method to make a good estimate of what the eigenvalue will converge to without having to make so many matrix multiplications?

[casinarro]

Okay so this helps get only one, the dominant eigen value