- A
diagonal matrix is one
whose off-diagonal
entries are all zero. A
superdiagonal entry is one that is
directly above and to the
right of the main diagonal...
- off-diagonal
entry equal to 1,
immediately above the main
diagonal (on the
superdiagonal), and with
identical diagonal entries to the left and
below them. Let...
- subdiagonal, and a
lower Hessenberg matrix has zero
entries above the
first superdiagonal. They are
named after Karl Hessenberg. A
Hessenberg decomposition is...
- diagonal. Hence, this
matrix is not diagonalizable.
Since there is one
superdiagonal entry,
there will be one
generalized eigenvector of rank
greater than...
- \\0&0&0&\ldots &1\\0&0&0&\ldots &0\end{bmatrix}}.} This
matrix has 1s
along the
superdiagonal and 0s
everywhere else. As a
linear transformation, the
shift matrix...
-
diagonal elements, and two of
length n − 1
containing the
subdiagonal and
superdiagonal elements. The
discretization in
space of the one-dimensional diffusion...
- finite-dimensional case.
Because there are non-zero
entries on the
superdiagonal,
equality may be violated. The
quasinilpotent operators is one class...
-
eigenvalues on the
leading diagonal, and
either ones or
zeroes on the
superdiagonal –
known as
Jordan normal form. Some
matrices are not diagonalizable...
- .., X - 1] b[] = main diagonal,
indexed from [0, ..., X - 1] c[] =
superdiagonal,
indexed from [0, ..., X - 2] scratch[] =
scratch space of
length X...
- only if T is
similar to a
matrix whose only
nonzero entries are on the
superdiagonal(this fact is used to
prove the
existence of
Jordan canonical form)....
