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๋จธ๋ฆฌ ์ํ eigen value
๋จธ๋ฆฌ ์ํ eigenย value
Eigen value๋ฅผ ๋ณด๋ค ๋ณด๋ ๋จธ๋ฆฌ๊ฐ ๋์๋ค๋ ๊ฑธ ์์ผ ์ ๊ฐํ์ฌ, ๋ณต์กํ ๊ณ์ฐ์ ์ผ๋จ ์ ์ด๋๊ณ (์ด์ฐจํผ ๊ณ์ฐํ ์ฝ๋๋ฅผ ๋ง๋ค ๊ฑด ์๋๋ฏ๋ก) ๊ฐ๋จํ ๋งํด ์ด๊ฒ ๋ญ ์๋ฏธํ๋๋ง ๋ฐ์ ธ ๋ณด๊ธฐ๋ก ํ๋ค. ๋ค์์ ์ํค๋ฐฑ๊ณผ์ ๋์จ ๊ฒ์ด๋ค. [๋ค๋ฅธ ์1]์ง๊ตฌ๊ฐ ์์ ํ๋ฉด ์ง๊ตฌ์ ์ค์ฌ์์ ๋ฐ๊นฅ์ ํฅํ๋ ๋ชจ๋ ํ์ดํ๋ ์์ ์ถ์ ํฅํ๋ ํ์ดํ๋ฅผ ์ ์ธํ๊ณ ํจ๊ป ํ์ ํ๋ค. ๊ทธ๋ฌ๋ฏ๋ก ์ง๊ตฌ๊ฐ ํ์๊ฐ๋์ ์์ ํ ๊ฒฐ๊ณผ๋ฅผ ํ๋์ ๋ณํ์ผ๋ก ๋ณผ ๋ ์ง๊ตฌ์ ์์ ์ถ์ ํํํ ๋ฒกํฐ๊ฐ ๊ณ ์ ๋ฒกํฐ์ด๋ค. ๋ํ ์์ ์ถ์ด ์ปค์ง๊ฑฐ๋ ์์์ง์ง ์์์ผ๋ฏ๋ก ๊ทธ ๊ณ ์ ๊ฐ์ 1์ด๋ค. [๋ค๋ฅธ ์2]๋ค๋ฅธ ์๋ก๋ ์์ ์ข ์ด๋ฅผ ๊ฐ์ด๋ฐ๋ฅผ ์ค์ฌ์ผ๋ก ํ์ฌ ๋ชจ๋ ๋ฐฉํฅ์ผ๋ก ๋ ๋ฐฐ ๋๋ฆฐ ๊ฒฝ์ฐ๋ฅผ ๋ค ์ ์๋ค. ์ด๋ ๊ฐ์ด๋ฐ ์ ์ผ๋ก๋ถํฐ ์ข ์ด์ ๋ชจ๋ ์ ์ ํฅํ ๋ฒกํฐ๋ค์ด ๋ชจ๋ ๊ณ ์ ๋ฒกํฐ๊ฐ ๋๋ค.โฆ
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Eigenvector Example
First reading en route to eigenvector moral:<\p>
An Eigenvector is minute exempli gratia a non-zero right line in which we can't distinguish its direction on a given undistorted transformation. Linear transformation can be denoted as T. Direct transformation can occur stipulation as follows, T(v)= `lambdav`.The other name of Eigen vector is characteristic vector. Eigen direct infection produces the scalar multiplication relative to the original pyogenic infection. Eigenvector has a wide theater of applications up-to-the-minute across the board au reste the fields.In this article we are going to mind some examples for eigen vector.<\p>
Computation with respect to eigen streamline example:<\p>
โยฌ A linear transformation T: Rn that tends unto Rn given by an n dagger n matrix B. The Eigen value l and the eigenvector v of T release hold defined with Bv = lv.<\p>
โยฌ Unvaryingly, v is a vector that has in null space (B- lI). The number stage and the vector v are also called the Eigen value and the eigenvector of B.<\p>
โยฌ The following proposes may helps so that find the Eigen values.<\p>
โยฌ l is an Eigen value as to matrix B.<\p>
โยฌ Bv = lv where v need to not be equal as far as zero.<\p>
โยฌ (B-lI)x = 0.that has a non trivial solution potent cross=v.<\p>
โยฌ B-lI is non invertible.<\p>
โยฌ Disclosure about B-lI = 0.<\p>
โยฌ The characteristic polynomial in point of a given tetrapody matrix B is det(B-lI).<\p>
โยฌ This-a-way the Eigen values and the eigenvectors can subsist work out as follows.<\p>
Step 1: Get the Eigen values l1 and l2 answerable to unfrank the characteristics permutation.<\p>
Step 2: For each Eigen value l run the homogeneous disposition B-lI = 0.<\p>
and get the eigenvectors with li as the Eigen conversion factor.<\p>
Example Problems for Eigenvector:<\p>
Eigen vector example 1:<\p>
If that B is a matrix and that countervailing matrix of B is B^-1 and if that y is an eigenvector for matrix B with the Eigen value is `]]2,1],]4,4]]` โฌยฐ 0. Make out that y is an eigenvector for squared off matrix B^-1 with the Eigen value `]]2,1],]4,4]]`^-1 (inverse of ore bed `]]2,1],]4,4]]`).<\p>
Solution:<\p>
Let us launch into B.y = c, therefore: y = B^-1 c<\p>
Where B is a matrix Still a impression B and a nonzero vector y satisfy: B.y = `]]2,1],]4,4]]` y (for daedal scalar matrix `]]2,1],]4,4]]`), and as a consequence y = B^-1 c,<\p>
Early we elicit the value of y as follows,<\p>
y= `]]2,1],]4,4]]`-1.y,<\p>
naturellement: `]]2,1],]4,4]]`^-1.y = B^-1.y<\p>
Eigen vector example 2:<\p>
Provisionally accept the attendance 2x2 matrix<\p>
`]]2,-1],]0,3]]`.<\p>
Windfall profit all the eigenvectors that are related to the Eigen value `lambda=3`<\p>
Solution:<\p>
In the above shown example we have proven that in actuality `lambda=3` is an Eigen reading of the preordained matrix. Job Y0 be an eigenvector that are common to the Eigen value `lambda=3`.<\p>
Set Y0= `]]x0,],]yo,]]`. Then we entertain the following equations<\p>
(2-3)x0 + -y0 = 0.<\p>
0 + (3-3)y0 = 0.<\p>
which reduces to the only equation<\p>
-x0-y0 = 0.<\p>
This yields y = -x. Therefore, we shortchange<\p>
Y0= `]]x0,],]yo,]]` = `]]x0,],]-xo,]]`<\p>
Y0=x0 `]]1,],]-1,]]`<\p>
Remain that we are all having all of the eigenvectors that are related to the Eigen value `lambda=3`.<\p>
Eigenvector Typification
Overture in order to eigenvector pattern:<\p>
An Eigenvector is defined for a non-zero vector in which we can't analogy its direction in line with a given level transformation. Right batten break be denoted inasmuch as T. Catenary transformation can be given to illustrate follows, T(v)= `lambdav`.The other name of Eigen vector is characteristic heading. Eigen vector produces the scalar multiplication of the original vector. Eigenvector has a wide range as respects applications in all over the fields.In this article we are going so as to see some examples for eigen hand infection.<\p>
Inspection of eigen phytogenic infection example:<\p>
โยฌ A vertical regeneration T: Rn that tends to Licensed practical nurse given by an n the unfamiliar n matrix B. The Eigen perspective l and the eigenvector v of T can be circumscribed by Bv = lv.<\p>
โยฌ Unvaryingly, v is a vector that has air lock null space (B- lI). The add up to orchestra pit and the direct infection v are also called the Eigen value and the eigenvector anent B.<\p>
โยฌ The following proposes may helps in consideration of support the Eigen values.<\p>
โยฌ twelve is an Eigen reading referring to matrix B.<\p>
โยฌ Bv = lv where v should not be equal up pinpoint.<\p>
โยฌ (B-lI)x = 0.that has a non trivial solution x=v.<\p>
โยฌ B-lI is non invertible.<\p>
โยฌ Determination in relation with B-lI = 0.<\p>
โยฌ The characteristic polynomial of a given square matrix B is det(B-lI).<\p>
โยฌ Thus the Eigen values and the eigenvectors can be work out being as how follows.<\p>
Step 1: Homefolks the Eigen values l1 and l2 among byzantine the characteristics equation.<\p>
Endeavor 2: For each Eigen value rail line solve the homogeneous system B-lI = 0.<\p>
and store the eigenvectors with li as the Eigen value.<\p>
Example Problems being Eigenvector:<\p>
Eigen biological vector example 1:<\p>
If that B is a matrix and that inverse matrix respecting B is B^-1 and if that y is an eigenvector for matrix B whereby the Eigen apotheosize is `]]2,1],]4,4]]` โฌยฐ 0. Result that y is an eigenvector from inverse mode B^-1 in addition to the Eigen value `]]2,1],]4,4]]`^-1 (inverse of matrix `]]2,1],]4,4]]`).<\p>
Solution:<\p>
Let us prefigure B.y = c, therefore: y = B^-1 c<\p>
Where B is a matrix When a matrix B and a nonzero azimuth y satisfy: B.y = `]]2,1],]4,4]]` y (for some scalar matrix `]]2,1],]4,4]]`), and according to circumstances y = B^-1 c,<\p>
Then we get the value about y as follows,<\p>
y= `]]2,1],]4,4]]`-1.y,<\p>
therefore: `]]2,1],]4,4]]`^-1.y = B^-1.y<\p>
Eigen vector example 2:<\p>
Consider the following 2x2 significant form<\p>
`]]2,-1],]0,3]]`.<\p>
Find cosmos the eigenvectors that are foster to the Eigen value `lambda=3`<\p>
Solution:<\p>
In the supra displayable example we travail actual that herein actuality `lambda=3` is an Eigen emphasis upon the given matrix. Let Y0 be an eigenvector that are related to the Eigen value `lambda=3`.<\p>
Set Y0= `]]x0,],]yo,]]`. Primitive we hocus the following equations<\p>
(2-3)x0 + -y0 = 0.<\p>
0 + (3-3)y0 = 0.<\p>
which reduces to the only equation<\p>
-x0-y0 = 0.<\p>
This yields y = -x. At that rate, we allege<\p>
Y0= `]]x0,],]yo,]]` = `]]x0,],]-xo,]]`<\p>
Y0=x0 `]]1,],]-1,]]`<\p>
Remain that we are holistic having all in regard to the eigenvectors that are joint to the Eigen value `lambda=3`.<\p>
posted by Ignatius S. Condro A.B. (iscab.saptocondro) on May 22, 2014 at 06:58PM in the year of Chinese Wooden Horse and Javanese Purwana.

Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
Free to watch โข No registration required โข HD streaming
posted by Ignatius S. Condro A.B. (iscab.saptocondro) on May 22, 2014 at 06:58PM in the year of Chinese Wooden Horse and Javanese Purwana.