Sure sir, I was going through an exam paper this morning then I found a question on this and I got stuck completely but am okay now you have really helped
Sir, the eigenvalues in my possession are 1, 1, 3. Given your guidance to prioritize selection in decreasing order along the diagonal, may I inquire which one should be of primary consideration?
Decreasing orders will be 3,1,1. For matrix P, the first column will be evector for 3. And for evalue 1, you have two evectors. So you keep these evectors in any order in columns 2 and 3 of the matrix P , doesn't matter.
No..not required... Only important thing is the sequence . Whatever sequence you r using for eigenvalues put the same sequence for the same corresponding eigenvectors. In SVD decomposition it matters...not here...
Sir I want one answer,in my book ([(2,1,0),(1,3,0),(0,0,2)]) symmetric matrix and its gn eigen value is 1,2,4 eigen vector (1,0,-1),(0,1,1),(0,1,0),but oi check it was wrong,so please send correct matrix for that sir,i want to know what is wrong in that Matrix
In this case , you P matrix will be first 3 columns and Diagonal matrix D will be 1,2,4 as the diagonal entries. Then P DP inverse will give us the matrix A... make sure to maintain the order of eigenvalues and eigenvectors.. I will try to do the calculations once I get free time..
sir i got a question telling me to find 3X3 matrix and they have given 2 eigne vectros and 3 eigen values out of which 2 are repeated how do i prove if the matrix is diagonalizable?
@vrundpatel3291 i have 2 questions:: 1. Are all the entries real or complex numbers allowed? 2. You are saying that eigenvalues are , say, a,a,b, and eigenvector for a is v, and for b is w.
@@DrMathaholic I'll just type out the question for you sir: For a symmetric matrix A, the eigen vectors are (1,1,1) and (1,-2,1) corresponding to eigen values x1=6 and x2=12. If x3=6, find A
@vrundpatel3291 symmetric matrices are orthogonally diagonalizable that means the matrix P is orthogonal. Eigenvectors of 6 are orthogonal to eigenvectors of 12. For 12, eigenvector is (1,-2,1) so take vector orthogonal to (1,-2 1). For ex. Take (-1,0,1). This is also orthogonal to first eigenvector of 6. Thus we have 3 orthogonal vectors and you have mateix P. Further P^-1 is nothing but P transpose.. so inverse of P is also easy to find..
sir we are given characteristic equation of matrix A instead of eigen values . after finding the eigen values using characteristic equation how will we know which eigen value corresponds to which eigen vectors???
That's what I told in this video. Your A = PDP^{-1}. Where D is diagonal matrix with eigenvalues as diagonal elements and P is a matrix whose column vectors are eigenvectors
Sir is there any restriction for using this method, like the matrix should be symmetric so and so . In my question paper they gave 3 eigen values and vectors . Shall I do same procedure to find matrix.
If Matrix is not given and eigenvectors are also not given.. Only Eigenvalues are given then its difficult to predict the matrix. Matrix can be anything
@Abinaya Arockiyaraja if evalues and evectors are given then find A. Once u have A, using characteristic polynomial we will have relation between A and powers of A ( by Cayley Hamilton theorem, see my video lecture on that)... from their u can find A inverse and powers of A.
I solved it by putting the eigenvalues from 1,2,3 and their eigenvector in order as eigenvalues and give me a totally different Matrix A , shouldn’t it be the same result of yours?
Finally able to understand how it works. Was having backlogs in iitm lectures but thanks to you...
All the best..
Finally I have found what I wanted thank you sir
Glad to hear that :)
Sure sir, I was going through an exam paper this morning then I found a question on this and I got stuck completely but am okay now you have really helped
Thank you, this helped me a lot, I was stuck on these types of questions and now, I know how go to solve them.
Thank you so much 💌
Happy to hear that..all the best 😊
Really healpful😊
Thank you.. 😊
Sir,At p matrix 1st column 3rd element is wrong.There should come 1,1,1 but you wrote 1,1,0.
Oh okay..May b while writing I might have made a mistake. Thank you for watching carefully and pointing it out😊
Sure but the most important thing is the concept of you have gotten it then you are good
Thank you so much Sir😊
@@shivrai5406 welcome. :)
Sir, the eigenvalues in my possession are 1, 1, 3. Given your guidance to prioritize selection in decreasing order along the diagonal, may I inquire which one should be of primary consideration?
Decreasing orders will be 3,1,1. For matrix P, the first column will be evector for 3. And for evalue 1, you have two evectors. So you keep these evectors in any order in columns 2 and 3 of the matrix P , doesn't matter.
@@DrMathaholic Thanks sir 🙏🏻
Sir, do we have to put the eigen values from highest to lowest ??
Sir plz tell me..
No..not required...
Only important thing is the sequence .
Whatever sequence you r using for eigenvalues put the same sequence for the same corresponding eigenvectors.
In SVD decomposition it matters...not here...
@@DrMathaholic Thank you so much for your help sir. 😊
@@No1likeme78 welcome. :)
Hello, do you have any video explaining how to get state space matrix representation form eigenvalues and eigenvectors, for matrices B , C and D?
What are the matrices B,C,D?
Is this method is applicable when two eigen values are same?
Yes, provided for these 2 same eigenvalues we have 2 linearly independent eigenvectors.. Algebraic multiplicity = geometric multiplicity
this was helpful thank you sir
Happy to hear that.. welcome 😊
Sir I want one answer,in my book ([(2,1,0),(1,3,0),(0,0,2)]) symmetric matrix and its gn eigen value is 1,2,4 eigen vector (1,0,-1),(0,1,1),(0,1,0),but oi check it was wrong,so please send correct matrix for that sir,i want to know what is wrong in that Matrix
In this case , you P matrix will be first 3 columns and Diagonal matrix D will be 1,2,4 as the diagonal entries.
Then P DP inverse will give us the matrix A... make sure to maintain the order of eigenvalues and eigenvectors..
I will try to do the calculations once I get free time..
@@DrMathaholic thank you sir
Danko is thank you
Welcome :)
sir i got a question telling me to find 3X3 matrix and they have given 2 eigne vectros and 3 eigen values out of which 2 are repeated how do i prove if the matrix is diagonalizable?
@vrundpatel3291 i have 2 questions::
1. Are all the entries real or complex numbers allowed?
2. You are saying that eigenvalues are , say, a,a,b, and eigenvector for a is v, and for b is w.
@@DrMathaholic I'll just type out the question for you sir:
For a symmetric matrix A, the eigen vectors are (1,1,1) and (1,-2,1) corresponding to eigen values x1=6 and x2=12. If x3=6, find A
@vrundpatel3291 symmetric matrices are orthogonally diagonalizable that means the matrix P is orthogonal. Eigenvectors of 6 are orthogonal to eigenvectors of 12. For 12, eigenvector is (1,-2,1) so take vector orthogonal to (1,-2 1). For ex. Take (-1,0,1).
This is also orthogonal to first eigenvector of 6.
Thus we have 3 orthogonal vectors and you have mateix P. Further P^-1 is nothing but P transpose.. so inverse of P is also easy to find..
@@DrMathaholic Thank you very much sir!
Thank you sir ❤
😊
Welcome 😊
Is there any logical explanation of taking that ,Matrix D and matrix P that as?
Yes, the concept of diagonalisation..
ruclips.net/video/XUmjhJgikxU/видео.html
sir we are given characteristic equation of matrix A instead of eigen values . after finding the eigen values using characteristic equation how will we know which eigen value corresponds to which eigen vectors???
After finding evalues, find evectors. Then you get the matrix P and D and ultimately u get A
Sir agar 2x2 ke matrix ka characteristic polynomial A²+3A+2 diya hai tab A matrix kaise find kare
Lengthy problem hai thoda.
Take A= [ a b and in the next line c d], iske square lo and use equation A^2+3A+2I =0 to find the values of a,b,c
Thank you
Welcome :)
Thank you!!!
Welcome 😊
How to calculate 3x3 matrix A, if one column of A is given, 2 eigenvalues and vectors are given and 3rd eigen vector and eigenvalue is unknown..
Write down eigenvectors as columns..you will have 3x3 matrix..it's determinant will be same as determinant of A.
how to find matrix A 2x2 out of eigen values & vectors?
That's what I told in this video. Your A = PDP^{-1}. Where D is diagonal matrix with eigenvalues as diagonal elements and P is a matrix whose column vectors are eigenvectors
Thankyou sir❤
Welcome 😊
Thanks !
Welcome 🙂
Sir is there any restriction for using this method, like the matrix should be symmetric so and so . In my question paper they gave 3 eigen values and vectors . Shall I do same procedure to find matrix.
No restriction..
Yes, Pls use this procedure...
Can anyone explain me how to calculate p inverse🙏🙏
Use the gauss elimination method to find the inverse...or you can use the formula involving adjoint and minor of a matrix...
Thanks sir 🙏
Welcome :)
what if you are given 2 eigen values but only 1 eigen vector for finding a 2 by 2 matrix
🙂
In that case, you can't use this method. Then Jordan canonical form comes into the picture.
Thanku so much sir,
I was a little bit confused in matrix D,
What to put in D except diagonal,
You cleared my doubt, thanku sir
Welcome.. 😊
Sir when only eigenvalues are given
If Matrix is not given and eigenvectors are also not given..
Only Eigenvalues are given then its difficult to predict the matrix. Matrix can be anything
@@DrMathaholic then how can i find A inverse and A^4 ? Sir
@Abinaya Arockiyaraja if evalues and evectors are given then find A. Once u have A, using characteristic polynomial we will have relation between A and powers of A ( by Cayley Hamilton theorem, see my video lecture on that)... from their u can find A inverse and powers of A.
THANK YOU SO MUCH SIR U HELPED MY FRIEND TOMMOROW IS OUR MIDSEM U SAVED OUR ASS SIR
All d best for exam...do well..
after 45 mins i have 4th end sem and i don't know how to calculate P inverse
@@jarvis9263 lesgooo bro
Sir, 👌
Thanks 😊
Row wise matrix I got. [12/5 -18/5 3/5 , 0 0 0 , 12/5 -18/5 3/5] pls verify
- 18/ 5 is not there it's -6/5 !! Someone pls verify rest all terms are same
I solved it by putting the eigenvalues from 1,2,3 and their eigenvector in order as eigenvalues and give me a totally different Matrix A , shouldn’t it be the same result of yours?
When u do PDP^{-1}, you should get A... I think, you might have made mistake while doing calculation ..can u check ur calculations again
@@DrMathaholic yes i think the mistake is i made the equation P^-1 D P ,, thank you!
@@heshamhanafy9232 👍🙂welcome
👏👏👏👏👏👏👏👏
Thanks 😊
Sir, do we need to write the eigenvectors in normalised form first to write P matrix?
Not compulsory...if in the Question they say to normalize then only .
P in calculation you wrote transverse sir
Ohh..
what timestamp?
Sorry sir I told wrongly ...
During substitution of P a31 position you wrote 0 instead of 1
@@maha_bgm_official8989 oh okay..
Good, that u understand and found the mistake. :)
🥰🔨
Sir please reply
🙏🙏🙏🙏
Good morning sir, provide me your email
Jatinmajithia@gmail.com
Thank you sir
Welcome 😊