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:
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:
“Knighterrantry is a most chuckleheaded trade, and it is tedious hard work, too, but I begin to see that there is money in it, after all, if you have luck. Not that I would ever engage in it, as a business, for I wouldn’t. No sound and legitimate business can be established on a basis of speculation. A successful whirl in the knighterrantry line—now what is it when you blow away the nonsense and come down to the cold facts? It’s just a corner in pork, that’s all.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“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)