Who exactly is "The Woman" in The Death Of A Salesman?

"The
Woman" is someone Willy is having an affair with.  Her presence feeds into the theme of
illusion vs. reality.  Biff thinks the world of his father, but doesn't know until it's too late
that his dad is cheating on his mom.  "The Woman" has been forced to hide in the
bathroom upon Biff's arrival because she is a secret herself.  She is "hidden" from
the rest of the family. She is completely different from Linda, the boys' mother.  Willy buys
gifts for "The Woman" like silk stockings, while Linda has to sew the holes in her own
stockings.