**Find Matrix A from eigenvalues and eigenvectors? Physics**

So here is my problem, Let A be a symmetric Matrix (2x2) with EV=(-2, 3) and the Eigenvalue being -5. Find the 2. Eigenvector to the second Eigenvalue.... We know from the definition of eigenvalues and eigenvectors, Ax = lambda x. Now that we’ve got our eigenvectors in the columns of the matrix S, and our eigenvalues are along the diagonal of Λ

**Find Matrix A from eigenvalues and eigenvectors? Physics**

Therefore, λ 2 is an eigenvalue of A 2, and x is the corresponding eigenvector. Now, if A is invertible, then A has no zero eigenvalues, and the following calculations are justified: so λ −1 is an eigenvalue of A −1 with corresponding eigenvector x .... We know we're looking for eigenvalues and eigenvectors, right? We know that this equation can be satisfied with the lambdas equaling 5 or minus 1. So we know the eigenvalues, but we've yet to determine the actual eigenvectors. …

**Finding the sec. Eigenvector when knowing the first**

In the context of Linear Algebra, one finds an eigenvalue of a matrix and then finds the right or the left eigenvector associated to that eigenvalue. Assume you have the matrix (your matrix) Assume you have the matrix (your matrix)... Eigenvalues and Eigenvectors, More Direction Fields and Systems of ODEs First let us speak a bit about eigenvalues. Defn. An eigenvalue λ of an nxn matrix A means a scalar (perhaps a complex number) such that Av=λv has a solution v which is not the 0 vector. We call such a v an eigenvector of A corresponding to the eigenvalue λ. Note that Av=λv if and only if 0 = Av-λv = (A- λI)v, where

**Ok I know how to find eigenvalues and eigenvectors but**

Therefore, λ 2 is an eigenvalue of A 2, and x is the corresponding eigenvector. Now, if A is invertible, then A has no zero eigenvalues, and the following calculations are justified: so λ −1 is an eigenvalue of A −1 with corresponding eigenvector x .... The eigenvector and eigenvalue represent the “axes” of the transformation. Consider spinning a globe: every location faces a new direction, except the poles. An “eigenvector” is an input that doesn’t change direction when it’s run through the matrix (it points “along the axis”).

## How To Find Eigenvalue Knowing Eigenvector

### Find Matrix A from eigenvalues and eigenvectors? Physics

- What are Eigenvalues and Eigenvectors? A must-know concept
- can eigenvector be found without computing the eigenvalue
- Ok I know how to find eigenvalues and eigenvectors but
- Finding the sec. Eigenvector when knowing the first

## How To Find Eigenvalue Knowing Eigenvector

### In the context of Linear Algebra, one finds an eigenvalue of a matrix and then finds the right or the left eigenvector associated to that eigenvalue. Assume you have the matrix (your matrix) Assume you have the matrix (your matrix)

- We know from the definition of eigenvalues and eigenvectors, Ax = lambda x. Now that we’ve got our eigenvectors in the columns of the matrix S, and our eigenvalues are along the diagonal of Λ
- We know we're looking for eigenvalues and eigenvectors, right? We know that this equation can be satisfied with the lambdas equaling 5 or minus 1. So we know the eigenvalues, but we've yet to determine the actual eigenvectors. …
- This is unusual behavior and earns the vector v and quantity λ special names: the eigenvector and eigenvalue. These are characteristic values of the matrix because multiplying the matrix by the eigenvector leaves the vector unchanged apart from multiplication by a factor of the eigenvalue.
- In the context of Linear Algebra, one finds an eigenvalue of a matrix and then finds the right or the left eigenvector associated to that eigenvalue. Assume you have the matrix (your matrix) Assume you have the matrix (your matrix)

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