Block Krylov subspaces correspond isometrically to matrix polynomial spaces, allowing transfer of Szegő recurrences and CMV frameworks to orthogonalize polynomial and extended block Krylov bases for unitary matrices.
Lund.A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors
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Block Krylov subspaces and orthogonal matrix polynomials: a structural correspondence with applications to unitary matrices
Block Krylov subspaces correspond isometrically to matrix polynomial spaces, allowing transfer of Szegő recurrences and CMV frameworks to orthogonalize polynomial and extended block Krylov bases for unitary matrices.