The Motzkin-Taussky theorem, proved by Theodore Motzkin and Olga Taussky-Todd in 1952, is a result in operator and matrix theory describing sums of two bounded linear operators, or equivalently two matrices, that are jointly diagonalizable in the sense that every linear combination of them is itself diagonalizable. Under that condition, the theorem shows the eigenvalues of any linear combination of the two operators must themselves be linear combinations of the two operators' own eigenvalues, a property the original authors called property L, with applications in perturbation theory.
Facts
StatementLet X be a finite-dimensional complex vector space and A,B in B(X) be such that all linear combinations T equals alpha A plus beta B are diagonalizable. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Motzkin-Taussky theorem (Wikipedia)
StatementQuote, Statement
Let X be a finite-dimensional complex vector space
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