Dominant eigenvectors of an unknown matrix

1. How do you find the dominant eigenvector of a matrix?
2. What is the dominant eigen value of the matrix?
3. What is a leading eigenvalue?

How do you find the dominant eigenvector of a matrix?

The Power Method is used to find a dominant eigenvalue (one having the largest absolute value), if one exists, and a corresponding eigenvector. To apply the Power Method to a square matrix A, begin with an initial guess u₀ for the eigenvector of the dominant eigenvalue.

What is the dominant eigen value of the matrix?

Matrix algebra

Λ₁ is known as the dominant eigenvalue, as it is the largest in magnitude, and Λ₂ is known as the sub-dominant eigenvalue, as it is the second largest in magnitude.

What is a leading eigenvalue?

The first eigenvalue is often called the "dominant" or "leading" eigenvalue. Eigenvalues are also often called "latent values". The eigenvalue is a measure of the strength of an axis, the amount of variation along an axis, and ideally the importance of an ecological gradient.