Euclidean Condition and Block Relative Gain: Connections, Conjectures, and Clarifications

Given an arbitrary nonsingular complex matrix, certain quantitative relationships between its Euclidean condition number and its associated block relative gains are established. In addition, an as yet unproven relation of this type is conjectured. The control theoretic implications of the established relations are briefly discussed, clarifying the role of the block relative gain concept in control theory.

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