Block tensors and symmetric embeddings

Understand

Well known connections exist between the singular value decomposition of a matrix A and the Schur decomposition of its symmetric embedding sym(A) = [ 0 A; A' 0].

• In particular, if s is a singular value of A then +s and -s are eigenvalues of the symmetric embedding.
• The top and bottom halves of sym(A)'s eigenvectors are singular vectors for A.
• Power methods applied to A can be related to power methods applied to sym(A).