J-orthogonal matrices arise in the analysis and numerical solution of various matrix problems involving indefinite inner products, including, in particular, the downdating of Cholesky factorizations.

By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution X̂, which is ...

Real inner products. Orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications ...