Poincaré separation theorem

In mathematics, the Poincaré separation theorem, also known as the Cauchy interlacing theorem, gives some upper and lower bounds of eigenvalues of a real symmetric matrix BTAB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B. The theorem is named after Henri Poincaré. More specifically, let A be an n × n real symmetric matrix and B an n × r semi-orthogonal matrix such that BTB = Ir.

Source: Wikipedia — Poincaré separation theorem (CC BY-SA 4.0)

Poincaré separation theorem

In mathematics, the Poincaré separation theorem, also known as the Cauchy interlacing theorem, gives some upper and lower bounds of eigenvalues of a real symmetric matrix BTAB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B. The theorem is named after Henri Poincaré. More specifically, let A be an n × n real symmetric matrix and B an n × r semi-orthogonal matrix such that BTB = Ir.

Source: Wikipedia "Poincaré separation theorem" · CC BY-SA 4.0

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