Isotropic Part and Degenerate Subspaces
Let, be subspaces of . The subspace for all is called the orthogonal companion of, and is the isotropic part of . If, is called non-degenerate; otherwise it is degenerate. If for all, then the two subspaces are said to be orthogonal, and we write . If where, we write . If, in addition, this is a direct sum, we write .
Read more about this topic: Indefinite Inner Product Space
Famous quotes containing the words part and/or degenerate:
“The greatest, or rather the most prominent, part of this city was constructed with the design to offer the deadest resistance to leaden and iron missiles that might be cast against it. But it is a remarkable meteorological and psychological fact, that it is rarely known to rain lead with much violence, except on places so constructed.”
—Henry David Thoreau (18171862)
“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other mens thinking.”
—Ralph Waldo Emerson (18031882)