  We develop K$\omega$, an open-source linear algebra library for the shifted
Krylov subspace methods. The methods solve a set of shifted linear equations
$(z_k I-H)x^{(k)}=b\, (k=0,1,2,...)$ for a given matrix $H$ and a vector $b$,
simultaneously. The leading order of the operational cost is the same as that
for a single equation. The shift invariance of the Krylov subspace is the
mathematical foundation of the shifted Krylov subspace methods. Applications in
materials science are presented to demonstrate the advantages of the algorithm
over the standard Krylov subspace methods such as the Lanczos method. We
introduce benchmark calculations of (i) an excited (optical) spectrum and (ii)
intermediate eigenvalues by the contour integral on the complex plane. In
combination with the quantum lattice solver $\mathcal{H} \Phi$, K$\omega$ can
realize parallel computation of excitation spectra and intermediate eigenvalues
for various quantum lattice models.
