In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr or At) created by any one of the following equivalent actions:
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Some articles on transpose:
... Ideally, one might hope to transpose a matrix with minimal additional storage ... This leads to the problem of transposing an n × m matrix in-place, with O(1) additional storage or at most storage much less than mn ...
... an invertible matrix P over the same field such that PTAP = B where "T" denotes the matrix transpose ... Note that Halmos defines congruence in terms of conjugate transpose (with respect to a complex inner product space) rather than transpose, but this definition has not been ...
... In the mathematical and algorithmic study of graph theory, the converse, transpose or reverse of a directed graph G is another directed graph on the same set of vertices with all of ... contains an edge (u,v) then the converse/transpose/reverse of G contains an edge (v,u) and vice versa ...
... Language/Library Create Determinant Transpose Element Column Row Eigenvalues Fortran m=RESHAPE(, SHAPE(m)) TRANSPOSE(m) m(i,j) m(,j) m(i,) Ch m ...
... Then the transpose (or dual) of T is an operator satisfying for all x in B1 and y in B2* ... The necessary and sufficient condition for the transpose of T to exist is that T is densely defined (for essentially the same reason as to adjoints, as discussed above.) For any Hilbert space H ... Through this isomorphism, the transpose T' relates to the adjoint T∗ in the following way , where ...
More definitions of "transpose":
- (verb): Put (a piece of music) into another key.
- (noun): A matrix formed by interchanging the rows and columns of a given matrix.
- (verb): Transpose and remain equal in value.
- (verb): Change key.
Example: "Can you transpose this fugue into G major?"
Famous quotes containing the word transpose:
“We have to transpose ourselves into this impressionability of mind, into this sensitivity to tears and spiritual repentance, into this susceptibility, before we can judge how colorful and intensive life was then.”
—Johan Huizinga (18721945)