Transpose Map

Some articles on map, transpose, transpose map:

Transpose of Linear Maps
... If f V → W is a linear map between vector spaces V and W with nondegenerate bilinear forms, we define the transpose of f to be the linear map tf W → V, determined by Here, BV and BW are the bilinear forms on V ... The matrix of the transpose of a map is the transposed matrix only if the bases are orthonormal with respect to their bilinear forms ... The transpose of a map between such spaces is defined similarly, and the matrix of the transpose map is given by the conjugate transpose matrix if the bases are orthonormal ...

Famous quotes containing the words map and/or transpose:

    Unless, governor, teacher inspector, visitor,
    This map becomes their window and these windows
    That open on their lives like crouching tombs
    Break, O break open,
    Stephen Spender (1909–1995)

    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)