Three Dimensions
For example, be a new basis given by its Euler angles. The matrix of the basis will have as columns the components of each vector. Therefore, this matrix will be (See Euler angles article):
Again, any vector of the space can be changed to this new basis by left-multiplying its components by the inverse of this matrix.
Read more about this topic: Change Of Basis, Change of Coordinates of A Vector
Famous quotes containing the word dimensions:
“The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.”
—Thomas Jefferson (1743–1826)
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)