What do these symbols mean? One looks like an inverse “T”, another looks like ^

I saw an equation as the following one.

• What is the meaning of the symbol looking like an inverse T?
• How about the symbol "^"?

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The following is the context:

This is the source:

On Updating Problems in Latent Semantic Indexing, SIAM Journal on Scientific Computing - 21(2):pp. 782-791;

• It might mean orthogonal complement, depending on what kind of an object $U_k$ is. – goblin Oct 25 '14 at 11:39
• Thanks. I think you are right. Orthogonal complement is a new concept to me. – Tyler 十三将士归玉门 Oct 25 '14 at 12:17
• How about the symbol "^"? – Tyler 十三将士归玉门 Oct 25 '14 at 12:23
• The "^" symbol is not universally defined. You'll have to reference the text to see exactly what it is. It may be that they wanted to call the matrix something different so rather than calling it "P" they called it "P hat". – NicNic8 Oct 25 '14 at 16:18
• I agree with @NicNic8, I think "P hat" is just meant to be treated as its own symbol, in much the same way as $x'$ is sometimes used as a symbol distinct from $x$. – goblin Oct 26 '14 at 13:24