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Works on Linear Algebra

Linear Algebra ×

22 results

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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Quadratic Forms

2026TheorySergey

Quadratic forms and their matrix, definiteness, Sylvester's criterion, and canonical form.
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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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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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Systems of Linear Equations

2026TheorySergey

Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.
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Matrix Rank

2026TheorySergey

Minors and the rank of a matrix, invariance of rank under elementary transformations, and a practical method for computing it.
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Inverse Matrices

2026TheorySergey

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

2026TheorySergey

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