Algebra¶
Hungerford. (1974). Algebra.
Cited by¶
1 citation across 1 artifact.
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Domain-specific¶
- Field (Algebraic)
- Linear algebra's central operations are all predicated on the scalar field: Gaussian elimination works because each non-zero pivot element has an inverse allowing the row to be normalised; the eigenvalue equation det(A − λI) = 0 produces eigenvalues in the scalar field (or requires a field extension such as ℂ to close it); and dimension theory — the fact that any two bases of a vector space over a field have the same cardinality — depends on the field structure to guarantee that basis-change matrices are invertible
This sourceA graduate algebra text proving that any two bases of a free module over a division ring have the same cardinality, and treating eigenvalues as elements of the scalar field.
Supported in partVerified against the work's full text
“Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text”
- Linear algebra's central operations are all predicated on the scalar field: Gaussian elimination works because each non-zero pivot element has an inverse allowing the row to be normalised; the eigenvalue equation det(A − λI) = 0 produces eigenvalues in the scalar field (or requires a field extension such as ℂ to close it); and dimension theory — the fact that any two bases of a vector space over a field have the same cardinality — depends on the field structure to guarantee that basis-change matrices are invertible
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