Алгебра 2, Листок 1
2026Problem sheetAlexey Ilyin
Задачные листки к курсам алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.
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170
Search results for “k-средних”
97 results
Basic Operations on Matrices
2026TheorySergey
Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.
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150
Determinant
2026TheorySergey
The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.
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190
Linear Operator
2026TheorySergey
A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.
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150
Change of Basis
2026TheorySergey
The change-of-basis matrix, recomputing a vector's coordinates and an operator's matrix, and the orthonormal case.
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220
Quadratic Forms
2026TheorySergey
Quadratic forms and their matrix, definiteness, Sylvester's criterion, and canonical form.
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160
The torsion component of the Picard scheme
2026OtherBogdan Zavyalov
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.
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500
Векторное произведение
2026OtherSergey
Ориентация тройки векторов, определение векторного произведения через длину, перпендикулярность и правую тройку, геометрический смысл (площадь параллелограмма), свойства с доказательствами и полный вывод формулы через определитель.
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90
A curiosity: “supersmooth” varieties
2026TheorySean Cotner
A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.
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120
Some examples of algebraic groups
2026TheorySean Cotner
Two pathological phenomena for algebraic groups over general bases — a group degenerating between the multiplicative and additive group across a DVR, and a non-affine identity component — built as centralizers in SL_n.
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180