Dictionary

transformation matrix en · NOUN

Meanings

1. A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ.
   • A transformation matrix of dimension n×m operates on a column vector of dimension m×1 to produce a row vector of dimension 1×n.
   • The 4x4 transformation matrices are conveniently used to convert various entities expressed in different coordinate systems into another. 2005, Gerard Kim, Designing Virtual Reality Systems: The Structured Approach, Volume 1, Springer, page 47:
   • 1968 [McGraw-Hill], Granino A. Korn, Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, 2000, Dover, page 414, Refer to Sec. 14.8-6 for a procedure yielding transformation matrices T with the desired properties.
   • 1963 [McGraw-Hill], Lawrence P. Huelsman, Circuits, Matrices and Linear Vector Spaces, 2011, Dover, page 191, We would like to make as many as possible of the elements of the transformation matrix equal zero.
   • Given a linear transformation T(x) in functional form, its transformation matrix can be constructed by applying T to each vector of the standard basis, then inserting the results into the columns of the new matrix.

Forms

Deriveds

wave transformation matrix

Translations (1)

fi kuvausmatriisi (matrix that represents a linear transformation)