Section 28.3 Terminology and notation
- submatrix
a matrix of smaller dimensions inside a larger matrix; also called a block
- block-diagonal form
a square matrix that can be divided into blocks in such a way that there is a sequence of square blocks in a diagonal pattern, and every other block is a zero matrix
- invariant subspace (under a square matrix A)
a (proper, nontrivial) subspace W of \R^n in which every vector \uvec{w} has the property that the vector A\uvec{w} is again in W\text{;} also called an A-invariant subspace
- independent subspaces
nontrivial subspaces W_1,W_2,\dotsc,W_\ell of a finite dimensional vector space V where, given a basis \basisfont{B}_1 for W_1\text{,} a basis \basisfont{B}_2 for W_2\text{,} etc., the set \basisfont{B}_1 \cup \basisfont{B}_2 \cup \dotsb \cup \basisfont{B}_\ell of all these basis vectors taken together is linearly independent
- complete set of independent subspaces
a collection of independent subspaces of a finite dimensional vector space V whose dimensions add up to \dim V