- In geometry, a
diagonal is a line
segment joining two
vertices of a
polygon or polyhedron, when
those vertices are not on the same edge. Informally, any...
- 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...
- 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...
- 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...
- finite-dimensional case.
Because there are non-zero
entries on the
superdiagonal,
equality may be violated. The
quasinilpotent operators is one class...
-
matrix with ones only on the
superdiagonal or subdiagonal, and
zeroes elsewhere. A
shift matrix U with ones on the
superdiagonal is an
upper shift matrix...
- 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)....
- .., X - 1] b[] = main diagonal,
indexed from [0, ..., X - 1] c[] =
superdiagonal,
indexed from [0, ..., X - 2] scratch[] =
scratch space of
length X...
- diagonal,
which is
filled with λ {\displaystyle \lambda } and for the
superdiagonal,
which is
composed of ones. Any
block diagonal matrix whose blocks are...
