CHAPTER FIVEVector Subspaces
5.1 COLUMN, ROW, AND NULL SPACES
The essence of mathematics is not to make simple things compli cated, but to make complicated things simple.
—S. GUDDEN
Everything should be made as simple as possible, but not simpler.
—ALBERT EINSTEIN (1879–1955)
KISS Principle: Keep It Simple, Stupid!
Introduction
In Example 5 of Section 2.4, we encountered avector space that was contained in a larger vector space and sharedwith the larger space its definitions of vector addition and scalar multiplication. This is a common phenomenon, deserving our special study.
DEFINITION
A subset in a vector space is a subspace if it is nonempty and closed under the operations of adding vectors and multipling vectors by scalars.
A subspace is nonempty ...
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