https://dmitryserikoff.com/tags/krylov/Recent content in Krylov on Dmitry SerikovHugoen-usMon, 06 Jul 2026 00:00:00 +0300https://dmitryserikoff.com/projects/resona/Mon, 06 Jul 2026 00:00:00 +0300https://dmitryserikoff.com/projects/resona/<p><strong>Resona</strong> is a Python library for comprehensive spectral analysis of operators without ever constructing or storing the full matrix — &ldquo;the FFT of operators.&rdquo;</p> <p>Everything runs on a single primitive: the matrix–vector product <code>v ↦ A·v</code>. From that alone, Resona extracts eigenvalues, densities of states, effective rank, pseudospectra and condition numbers; composes operators algebraically via free probability (Pastur subordination, Brown measure for non-Hermitian operators); and even synthesizes new operators matching target spectral properties.</p>