Derivation: Casida Hermitian rewrite
Derivations
The Casida block equation has an indefinite metric — the right-hand
side mixes +𝟙 and −𝟙 — so it isn't a standard Hermitian eigenvalue
problem. This page walks through six algebraic steps that turn it into
one. Arrow keys (or the buttons below) step forward and back. Each step
shows the previous equation dimmed above the current one, and the bold
label between them names the algebraic move you just performed — the
thing a paper derivation usually makes you spot for yourself.
Two modes:
The "Multi-step" view (default) shows the six major milestones. The "Every step" toggle in the top-left expands them into every micro algebraic move — useful when a milestone hides too much work for you to verify mentally. Switch freely; the walker keeps your position.
Step 1 of 6 · ← → keys to navigate
Step 1
The Casida block equation. The right-hand side has an indefinite metric (the on the lower diagonal), so this isn't a standard Hermitian eigenvalue problem yet. The whole derivation is the work of massaging it into one.