
Slide 1
... • Let me say again what the word space means. It is a bunch of vectors, but not any bunch of vectors, it has to allow me to do the operations that vectors are for (add vectors and multiply by numbers, i.e. linear combination). • Of course, the results of such operations MUST lie also in that space! ...
... • Let me say again what the word space means. It is a bunch of vectors, but not any bunch of vectors, it has to allow me to do the operations that vectors are for (add vectors and multiply by numbers, i.e. linear combination). • Of course, the results of such operations MUST lie also in that space! ...
X. A brief review of linear vector spaces
... The set of all linear combinations formed from a fixed collection of vectors is a subspace of the original space. The fixed vectors are said to span the subspace. A basis for a vector space is a linearly independent set of vectors that spans the space. If the number of vectors in the space is finite ...
... The set of all linear combinations formed from a fixed collection of vectors is a subspace of the original space. The fixed vectors are said to span the subspace. A basis for a vector space is a linearly independent set of vectors that spans the space. If the number of vectors in the space is finite ...
quaternions slides
... AB != BA (in general) Multiplication is not commutative Implications for coordinate transforms: We can gather transforms into a single matrix We must do elementary transforms in the proper order – translate then scale != scale then translate ...
... AB != BA (in general) Multiplication is not commutative Implications for coordinate transforms: We can gather transforms into a single matrix We must do elementary transforms in the proper order – translate then scale != scale then translate ...