Coordinate Vector - Basis Transformation Matrix

Basis Transformation Matrix

Let B and C be two different bases of a vector space V, and let us mark with the matrix which has columns consisting of the C representation of basis vectors b₁, b₂, ..., b_n:

$_{C}^{B} = \begin{bmatrix} \ _C & \cdots & _C \ \end{bmatrix}$

This matrix is referred to as the basis transformation matrix from B to C, and can be used for transforming any vector v from a B representation to a C representation, according to the following theorem:

If E is the standard basis, the transformation from B to E can be represented with the following simplified notation:

where

and

Read more about this topic: Coordinate Vector

Famous quotes containing the words basis and/or matrix:

“It was the custom
For his rage against chaos
To abate on the way to church,
In regulations of his spirit.
How good life is, on the basis of propriety,
To be followed by a platter of capon!”
—Wallace Stevens (1879–1955)

““The matrix is God?”
“In a manner of speaking, although it would be more accurate ... to say that the matrix has a God, since this being’s omniscience and omnipotence are assumed to be limited to the matrix.”
“If it has limits, it isn’t omnipotent.”
“Exactly.... Cyberspace exists, insofar as it can be said to exist, by virtue of human agency.””
—William Gibson (b. 1948)