Formes quadratiques réelles semi-définies. Démonstration élémentaire du critère des mineurs principaux. (Real semi-definite quadratic forms. Elementary proof of the principal minors criterion) (Q913908)
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scientific article; zbMATH DE number 4148325
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Formes quadratiques réelles semi-définies. Démonstration élémentaire du critère des mineurs principaux. (Real semi-definite quadratic forms. Elementary proof of the principal minors criterion) |
scientific article; zbMATH DE number 4148325 |
Statements
Formes quadratiques réelles semi-définies. Démonstration élémentaire du critère des mineurs principaux. (Real semi-definite quadratic forms. Elementary proof of the principal minors criterion) (English)
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1987
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Using the two lemmas: (1) In every symmetric matrix of rank r there exists a non-singular \(r\times r\) submatrix, (2) If all principal minors of real symmetric non-singular matrix are \(\geq 0\) then they are in fact \(>0;\) the author extends the well known criterion for a real symmetric matrix to be positive definite namely that all principal minors be positive to positive semidefinite matrices, thus avoiding the limiting process usually employed.
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quadratic forms
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principal minors criterion
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real symmetric matrix
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positive definite
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