Changed selection of shift-and-invert mode in eigs. Added test for inverse iteration. Docs updated.
Change default of sigma to nothing.
Only non-empty sigma selects shift and invert mode (implies which=LM). Test updated.
Update NEWS.md
Document eye(A) when A is a dense/sparse matrix
New semantics of sigma in eigs(A, sigma)

- `sigma==nothing` specifies forward iteration (ARPACK `iparam(7)=1`), and a numeric real or complex sigma specifies inverse iteration with level shift (`iparam(7)=3` or 4 depending on `complexOP`)
Update documentation of eigs

- Specifies _all_ the valid values of the `which` keyword in a table.
- Updates `sigma` to its new default and semantics.
- Clarify interaction of `sigma` and `which` keywords via the type of linear operator that is constructed and passed to ARPACK.
Merge pull request #6053 from JuliaLang/pr/5776

Default to shift-and-invert mode for eigs for numeric sigma