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, ..., bn:

_{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:

    “The basis of optimism is sheer terror.”
    —Oscar Wilde (1854–1900)

    “As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
    —Margaret Atwood (b. 1939)