What is eigenspace basis?

An eigenspace basis is a set of vectors that span the eigenspace corresponding to a specific eigenvalue of a matrix. An eigenspace is the set of all eigenvectors associated with a specific eigenvalue.

The term basis refers to a set of linearly independent vectors that can be used to represent any vector in a space. Thus, an eigenspace basis is a set of linearly independent eigenvectors that can be used to represent any vector in the eigenspace corresponding to a specific eigenvalue.

In general, a matrix can have multiple eigenvalues and eigenspaces, and each eigenspace can have multiple eigenvectors. However, for each eigenspace there is always a basis of linearly independent eigenvectors, which can be used to diagonalize the matrix.

Eigenspace basis is important in many applications of linear algebra, including engineering, physics, and computer science. It is used to analyze the behavior of linear transformations, such as rotations and stretching, and to find solutions to systems of linear equations.