3x3 third-order matrix eigenvector calculator

Matrix A =
Scalar matrix (Z=c×I)=
|A| =
The trace of matrix A =
 
Singular matrix (A - c×I) =
 
|A - c×I| =
Eigenvalue c1 =
+ i
Eigenvalue c2 =
+ i
Eigenvalue c3 =
+ i
The value of c1 at the eigenvector (x,y,z) =
The value of c2 at the eigenvector (x,y,z) =
The value of c3 at the eigenvector (x,y,z) =

In mathematics, an eigenvector of a linear transformation is a non-degenerate vector whose direction remains unchanged under the transformation. The scale at which the vector is scaled under this transformation is called its eigenvalue. A linear transformation can usually be fully described by its eigenvalues ​​and eigenvectors. The eigenspace is a set of eigenvectors with the same eigenvalue. The word "characteristic" comes from the German word eigen. Hilbert first used this word in this sense in 1904, and Helmholtz used it in a related sense earlier. The word eigen can be translated as "own", "specific to", "characteristic", or "individual". This shows how important eigenvalues ​​are in defining specific linear transformations.