- #1
scholesmu
- 3
- 0
A= (3 0
0 3 )
why is it diagonalizable?
i'm not sure...
0 3 )
why is it diagonalizable?
i'm not sure...
A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix through a similarity transformation. This means that the matrix can be represented as a diagonal matrix with all zero entries except for the main diagonal.
A matrix is diagonalizable if it has n distinct eigenvalues, where n is the size of the matrix. This can be determined by finding the eigenvalues and eigenvectors of the matrix and checking if they are linearly independent.
A diagonalizable matrix is easier to work with and has many useful properties, such as being easier to compute powers and inverses of the matrix. It also allows for simpler analysis of the matrix's behavior and relationships with other matrices.
No, only square matrices can be diagonalizable since the similarity transformation requires the same number of rows and columns.
Not necessarily. A matrix can be diagonalizable but not invertible, as long as it has at least one eigenvalue equal to zero. In this case, the matrix will have a zero determinant and will not have an inverse.