- #1
himurakenshin
- 21
- 0
How can i find the eigen value(s) of A - (alpha)I
where A is an arbitrary matrix ?
where A is an arbitrary matrix ?
yes I know this, but I don't know how to find the eigen value of that paticular matrix (A can be any matrix). The actual question is that I have to prove that lambda is an eigen value of A only if (lamda - alpha) is an eigen value of Cmatt grime said:the eigenvalues of any square matrix, call it M, are the roots of the polynomial in x
det(M-xI)
An eigenvalue is a scalar value that represents how a matrix will act on a vector. It is often denoted by the Greek letter lambda (λ) and is a key concept in linear algebra.
Finding eigenvalues allows us to understand the behavior of a matrix and its associated linear transformation. It also helps in solving systems of linear equations and in many other applications, such as data compression and machine learning.
To find the eigenvalues of an arbitrary matrix, we need to solve the characteristic equation, which is the determinant of the matrix minus a scalar multiplied by the identity matrix. This equation will have roots that represent the eigenvalues of the matrix.
No, not all matrices have eigenvalues. A matrix must be square (same number of rows and columns) to have eigenvalues. Additionally, a matrix must also be invertible (have a non-zero determinant) to have eigenvalues.
Eigenvalues and eigenvectors are closely related. Eigenvectors are the vectors that are transformed only by a scaling factor when multiplied by a matrix, and the corresponding eigenvalues represent the magnitude of the scaling factor. In other words, eigenvectors are the directions along which a matrix acts only by stretching or shrinking, and eigenvalues are the amount by which it stretches or shrinks those eigenvectors.