This is what i have been looking for all semister!!!
@wes9627 Жыл бұрын
Thank you for this video. I learned what I needed. However, there is a much easier way to solve for the eigenvectors, which is related to LU factoring a matrix. And also to obtain an orthonormal transformation matrix from normalized eigenvectors. Let me demonstrate using the matrix equation associated with lambda = 3. The matrix equation is repeated here for illustration | 0 -1 1| |x| |-1 2 -1| |y| = 0 Eq. (1) | 1 -1 0| |z| Pick the absolutely largest entry in this matrix, in this case 2, as the pivotal element. If there are two or more absolutely largest entries, pick one with the most nonzero entries in its row. The row and column containing the pivotal element are the pivot row and pivot column. Scale the pivot row respectively by the ratio of each nonzero entry in the pivot column to the pivotal element. Thus divide the row 1, column 2 entry, -1 by 2 to get -1/2 and multiply pivot row 2 by (-1/2) to get |1/2, -1, 1/2| Then subtract this row from row 1 to get |-1/2, 0, 1/2| In a similar manner divide the row 3, column 2 entry by 2 to again get -1/2, scale the pivot row, and subtract this row from row 3 to get |1/2, 0, -1/2| Form a new matrix | -1/2 0 1/2| |x| | -1 2 -1 | |y| = 0 Eq. (2) | 1/2 0 -1/2| |z| Now strike the pivot row 2 and pivot column 2 from Eq. (2) to get | -1/2 1/2| |x| = 0 Eq. (3) | 1/2 -1/2| |z| Since all entries have the same absolute magnitude, pick the row 1, column 1 entry, -1/2 as the next pivotal element. Then scale pivot row 1 by (1/2)/(-1/2) and subtract from row 2 to get |0 0| and the modified matrix equation | -1/2 1/2| |x| = 0 Eq. (4) | 0 0 | |z| From Eq. (4) we have z - x =0 and from the second equation in Eq. (2) we have -x + 2y -z = 0, which give x = z and y = (x+z)/2. Since we have two equations and three unknowns, one value can be arbitrarily set, say set z = 1. Then x = z = 1 and y = (x+z)/2 = (1 + 1)/2 = 1. To get an orthonormal transformation matrix from the three eigenvector solutions, each eigenvector should be normalized to unity. The current magnitude of this eigenvector is sqrt(x^2 + y^2 + z^2) = sqrt (1^2 + 1^2 + 1^2) = sqrt(3) Thus the normalized eigenvector would be | 1/sqrt(3), 1/sqrt(3), 1/sqrt(3) |^T or | sqrt(3)/3, sqrt(3)/3, sqrt(3)/3 |^T When the 3 by 3 matrix is composed of three normalized eigenvectors, it is orthonormal and its inverse is equal to its transpose, which eliminates the need to compute a complex matrix inverse.
@wes9627 Жыл бұрын
Since the determinant of this symmetric matrix is 36 it is also positive definite. A positive definite matrix has all nonzero and positive eigenvalues. And the product of its three eigenvalues is also 36, so a good starting estimate for an eigenvalue would be the cube root of 36 or about 3.3. Synthetic division is only a good way to solve for the first eigenvalue when the values are nice, as in this example. An iterative Newton-Raphson method would be faster and easier. Let y = x^3-s1x^2+s2x-s3 and y' = 3x^2-2s1x+s2. Then dx = -y/y' and x
@lawrencejelsma81187 ай бұрын
I get so use to Gaussian elimination to find the eigenvectors of corresponding eigenvalues (and assigning 1 for independent variable rows) it is neat seeing someone applying Cramer's sort of thing on two rows with column blocking for x/|..| = -y/|..| = z/|..| way of doing it.
@vanshrajput5363 Жыл бұрын
Sir what will we do if any diagonal elements have -ve sign then we ignore and add all diagonal elements or we add all elements with -ve sign
@thanuja5128 Жыл бұрын
PtransposeA p how to find in calculator using like 1 divided by root 2
@surajdilare58872 ай бұрын
Bhaiya ke problem ho rahi hai question me jab crammerce rule lagate hai to x=y=z jab likjte hai to kya sirf y me minus aayega?????? Or xYz ke cofficient nahi lenge kya crammerce rule lagate samay?
@ayusuf16 Жыл бұрын
Does this method have a name? By the way, video helped me much .Thank you.
@gamersstop585 Жыл бұрын
learnt eigen value, eigen vector, Synthetic Division, cramer's rule ( cross multiplication ), Diagonalization in less than 20 mins 😭😭 dude is a life save 💫🫂
@nitinprabhu2912 жыл бұрын
Thank you so much bro ❤️❤️❤️❤️ valuable video thank you 🎉🎉🎉🎉
@UPSC2025-MATHS.OPTIONAL2 жыл бұрын
Sir cooefficent ke aage aap ne 2 kha se lia
@MdKhezarAhmed9 ай бұрын
2:35 in case if we got the trace in -minus? Will the it become +11
@MATHSPEDIAabhi9 ай бұрын
Yes
@jamunasjaanu95106 ай бұрын
Sir how to find P inverse in calsi plz can u send the video
@ch.meghana2994 Жыл бұрын
Sir plz give vedio this problem solve by orthogonal reduction method sir
@LemiTola7 ай бұрын
Please prepare video about Markov chain rule
@MATHSPEDIAabhi7 ай бұрын
Sure
@lakshyasingh7074 Жыл бұрын
11:39 Sir in case 1 where lambda is equal to 2 value of x should be -1 and z should be 1.
@MATHSPEDIAabhi Жыл бұрын
No x value is 1 and z value is 1.Make coefficient of x and z as +1.So I have taken z coefficient in the denominator (-1).
@myamuna738011 ай бұрын
Sir last lo aha values ravadhumledhu ga 2,3,6
@shivadylne15573 жыл бұрын
Thanks sir.. for easy understanding teaching
@altafmohammed1364 Жыл бұрын
Tq sir I understood
@naraboinaravichandra86592 жыл бұрын
How the s3value came sir
@sanitmajumder7209 Жыл бұрын
Chracteristic equation e ses er constant duto 36 er jagay 37,38 hoga
@fmncpfmncp8863 Жыл бұрын
bhi hindi my bola kry ya urdu
@prashanthjatothu4915 Жыл бұрын
Wonderfull explanation bro
@myamuna738011 ай бұрын
Sir lpl=-6 kada meru 6. Veasaru
@MATHSPEDIAabhi11 ай бұрын
|p|= 6 correct 💯
@myamuna738011 ай бұрын
Ok
@DilshadaIshaq3 ай бұрын
P inverse ksy nickla ap na
@MATHSPEDIAabhi3 ай бұрын
@@DilshadaIshaq determinant(P)/adjoint(P)
@nguhengkuen81452 жыл бұрын
thanks sir it really helps me a lot
@famiajaved2393 Жыл бұрын
Yoy are great
@aswathyms92232 жыл бұрын
Thank u sir♥
@PANADOL695 Жыл бұрын
I think sir u have made a mistake When applying Cramer rule ( the answer wa -1 1 -1 In the second part when lamda is equal to 3 But u had written 1 1 1 in the p 😅
@MATHSPEDIAabhi Жыл бұрын
Lamda =3 ,it is [1 1 1], check 15:21
@PANADOL695 Жыл бұрын
@@MATHSPEDIAabhisir that's the confusion The value of x y z are -1,1,-1 But in a column form 1,1,1
@MATHSPEDIAabhi Жыл бұрын
@@PANADOL695 "y" is having (-) as coefficient,when it is taken down in the Denominator it becomes (+1) so it will be [-1 -1 -1] and you can eliminate (-) sign since all elements have (-) sign so it becomes [1 1 1].
@PANADOL695 Жыл бұрын
@@MATHSPEDIAabhi sir thank u so much it was a confusion But I get it now Thank a lot 🥹
@myamuna738011 ай бұрын
Sir pls e sum calsi lo cheyandhi pls
@MATHSPEDIAabhi11 ай бұрын
Next video sure👍
@BindhuKamatham7 күн бұрын
For this problem find A power 4
@hiphopgaming77yt26 күн бұрын
S3 ❔
@sweety47_4511 ай бұрын
E concept ni Casio lo chesi chupiyandi
@MATHSPEDIAabhi11 ай бұрын
Ok 👍 next video
@kun7170 Жыл бұрын
Loveeeeeeeeeeee ❤❤
@MdBilalRaza8227 ай бұрын
Hindi me bana liya karo vedio
@godgaming40432 жыл бұрын
😃
@kwitondaematus41012 жыл бұрын
More grantiful
@MUHAMMADYAQOOBWAKO-dl2gz3 ай бұрын
Bhai meri agr english nhi ati toh hindi main bol le teri awaz h samjh nhi a rahi