What is Eigen vector: Definition and 16 Discussions
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by
λ
{\displaystyle \lambda }
, is the factor by which the eigenvector is scaled.
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.
Homework Statement
r1= 2 7
r2=-1 -6
Homework Equations
A-lambda*I=0
(A-lambda*I)*x=0
The Attempt at a Solution
I have got following eigen values:
lambda1 = -5 and lambda2=1
A-lambdaI matrix is:
r1 = 7 7
r2 = -1 -1
and x matrix is:
r1 =x
r2 =y
I can't understand why we have to use...
Hi all,
I think I have an idea of how the Mathematical aspects of Face recognition work. But I am curious as to what an eigenvector would be in this respect. I am trying to understand it through finding out how pixels are encoded: What map takes a pixel into a collection of...
Let's say we have a set of eigenvectors of a certain n-square matrix. I understand why the vectors are linearly independent if each vector belongs to a distinct eigenvalue.
However the set is comprised of subsets of vectors, where the vectors of each subset belong to the same eigenvalue. For...
When we are measuring the spin of the electron in the experiment, we choose the spin property as its eigen state for the measurement. The eigen vectors corresponding to these states could be time dependent. Can we still break the problem into solving time independent Schrodinger Equation and...
Homework Statement
Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x.
A =
4 4 2
* * *
* * *
x =
2
-1
10
Given that x is an eigenvector of the matrix A, what is the corresponding eigenvalue?
Homework EquationsThe Attempt at a Solution
4−λ 4 2
a...
The Cayley-Hamilton Theorem can be used to express the third invariant of the characteristic polynomial obtained from the non-trivial solution of the Eigenvector/Eigenvalue problem. I follow the proof (in Chaves – Notes on Continuum Mechanics) down to the following equation, then get stuck at...
I have had no problem while finding the eigen vectors for the x and y components of pauli matrix. However, while solving for the z- component, I got stuck. The eigen values are 1 and -1. While solving for the eigen vector corresponding to the eigen value 1 using (\sigma _z-\lambda I)X=0,
I got...
Homework Statement
Let M be a symmetric matrix. The eigenvalues of M are real and further M can be
diagonalized using an orthogonal matrix S; that is M can be written as
M = S^-1*D*S
where D is a diagonal matrix.
(a) Prove that the diagonal elements of D are the eigenvalues of M...
Homework Statement
I've done part A, and part D is easy. I'm stuck with part B. I have no idea what a "right hand side vector" is...
Homework Equations
The Attempt at a Solution
Part A: All eigenvectors are valid. Eigenvalues are 1, 1/2 and 1/3.
Homework Statement
Hi, for the matrix A =
0 1 0
1 0 0
0 0 2
I have calculated the eigen values, and have successfully calculated the eigen vectors for lamda = -1 and 1. However for...
Homework Statement
im trying to find the eigen vector for these 2 matrices: A=[0,0;0,8] AND A=[-8,0;0,0]
Homework Equations
The Attempt at a Solution
BACICALLY WHAT IM DOING IS "GUESSING" AT What x1, is then I am coming up wth the solution to x2 once I've made my guess for x1. how...
Homework Statement
Find the eigenvector for each of the matrices
Homework Equations
I have a 2X2 matrice. (4, 2) which are on the top and (2,1) which are on the bottom. I understand how to get the value of the eigen, but I am confused about getting the vector.
The Attempt at a...
I have some question on energy eigenvalue and eigenfunction
help please
A particle, mass m , exists in 3 dimensions, confined in the region
0< x < 2L, 0 < y < 3L, 0 < z < 3L
a) what are the energy eigenvalues and eigenfunctions of the particle?
b) if the particel is a...