Search results for “computer-science”

The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.

Nonsingular matrices, the invertibility criterion, the adjugate-matrix formula, and the Gauss–Jordan method.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.

The basic properties of addition, scalar multiplication, transposition, and multiplication of matrices, with justifications.