- #1
junglebeast
- 515
- 2
Wikipedia defines the Shur decomposition of matrix A as
A = Q U Q^{-1}
where Q is unitary and U is upper triangular.
http://en.wikipedia.org/wiki/Schur_decomposition
Mathworld defines the Shur decomposition of matrix A as
Q^H A Q = T,
where Q is unitary and T is upper triangular.
http://mathworld.wolfram.com/SchurDecomposition.html
Because Q is unitary, the inverse is the same as the conjugate transpose...but they still seem like completely different definitions because the matrix is either on the inside or the outside. What's the truth?
A = Q U Q^{-1}
where Q is unitary and U is upper triangular.
http://en.wikipedia.org/wiki/Schur_decomposition
Mathworld defines the Shur decomposition of matrix A as
Q^H A Q = T,
where Q is unitary and T is upper triangular.
http://mathworld.wolfram.com/SchurDecomposition.html
Because Q is unitary, the inverse is the same as the conjugate transpose...but they still seem like completely different definitions because the matrix is either on the inside or the outside. What's the truth?