# What is transpose?

• (verb): Transfer a quantity from one side of an equation to the other side reversing its sign, in order to maintain equality.

## Transpose

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:

### Some articles on transpose:

Transpose - Implementation of Matrix Transposition On Computers
... 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 ...
Matrix Congruence
... 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 ...
Transpose Graph
... 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 ...
Comparison Of Programming Languages (array) - Vectorized Array Operations - Mathematical Matrices Management
... 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 ...
Closed Operator - Transpose
... 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.
Synonyms: commute
• (verb): Change key.
Example: "Can you transpose this fugue into G major?"
• (verb): Change the order or arrangement of.
Example: "Dyslexics often transpose letters in a word"
Synonyms: permute, commute

### 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 (1872–1945)