- #1
brownman
- 13
- 0
How come a square matrix has eigenvalues of 0 and the trace of the matrix?
Is there any other proof other than just solving det(A-λI)=0?
Is there any other proof other than just solving det(A-λI)=0?
A rank 1 matrix is a square matrix where all the columns are multiples of each other, resulting in a one-dimensional column space.
To find the eigenvalues of a rank 1 matrix, you can simply take the single non-zero column and use it as the eigenvector. This means that the eigenvalue will be equal to the only non-zero entry in that column.
No, a rank 1 matrix can only have one eigenvalue. This is because the matrix only has one linearly independent column, so there is only one possible eigenvector and eigenvalue.
The eigenvalues of a rank 1 matrix represent the scaling factor of the single non-zero column. This means that the matrix only has one possible direction of transformation, and the eigenvalue determines the magnitude of that transformation.
No, a rank 1 matrix cannot have a zero eigenvalue. This is because the eigenvalue is equal to the only non-zero entry in the single column, and a rank 1 matrix, by definition, cannot have any zero entries.