Abstract
By discussing the level crossings (LC) of a hyperfine multiplet in external magnetic or electric fields, we find that the theory of matrix pencils is an appropriate mathematical formalism for general investigations on LC phenomena. Magnetic (electric)-field position and state vectors of a hyperfine LC correspond to a latent root and a latent vector of a regular matrix pencil. The theory enables us to give a general account of the orthogonality relations introduced recently, to derive sum-rule like limitations of the amplitudes of LC signals, and to present a method for a straightforward calculation of positions and state vectors of LC's.
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