Collection of problems in analytical geometry and linear algebra

[1939/73%]

L. A. Beklemisheva, D. V. Beklemishev, A. Y. Petrovich, I. A. Chubarov

Chapter 1Vectors and coordinates[173/84%]

Section 1Linear relations[53/79%]

Section 2The scalar product of vectors[50/86%]

Section 3Vector and mixed products of vectors[40/75%]

Section 4Change of basis and coordinate system[30/100%]

Chapter 2Line and plane[164/98%]

Section 5A line on a plane[67/99%]

Section 6Plane and a line in space[97/98%]

Chapter 3Quadratic curves[120/83%]

Section 7Geometric properties of second-order curves and their canonical equations[65/89%]

Section 8Tangents to conic sections[33/79%]

Section 9General theory of second-order curves[22/73%]

Chapter 4Quadric surfaces[111/73%]

Section 10Set equations in space and elementary theory of second-order surfaces[88/72%]

Section 11General theory of surfaces of the second order[23/78%]

Chapter 5Plane transformations. Groups[116/71%]

Section 12Linear and affine transformations of the plane[89/73%]

Section 13The concept of groups[27/63%]

Chapter 6Matrices[227/61%]

Section 14Determinants[44/64%]

Section 15Matrix operations[141/59%]

Section 16Matrix rank[42/64%]

Chapter 7Systems of linear equations[75/81%]

Section 17Systems of linear equations with a determinant different from 0[6/83%]

Section 18Systems of linear homogeneous equations[20/85%]

Section 19Systems of linear equations of general form[49/80%]

Chapter 8Linear spaces[64/78%]

Section 20Examples of spaces. Basis and dimension[34/91%]

Section 21Sum and intersection of subspaces[17/35%]

Section 22Complex linear spaces[13/100%]

Chapter 9Linear mappings and transformations[252/71%]

Section 23Main properties of linear mappings and transformations[104/71%]

Section 24Invariant subspaces, eigenvectors, and eigenvalues of linear transformations[148/71%]

Chapter 10Euclidean and unitary spaces[161/70%]

Section 25Scalar product. Gram matrix[58/74%]

Section 26Geometry of Euclidean space[74/72%]

Section 27Unitary spaces[29/55%]

Chapter 11Linear transformations of Euclidean and unitary spaces[152/52%]

Section 28Examples of linear transformations of Euclidean space. Adjoint transformation[37/65%]

Section 29Self-adjoint and orthogonal transformations[71/42%]

Section 30Linear transformations of a unitary space[44/57%]

Chapter 12Functions on a linear space[97/74%]

Section 31Linear functions[50/82%]

Section 32Bilinear and quadratic functions[47/66%]

Chapter 13Affine and point Euclidean spaces[81/62%]

Section 33Affine spaces[44/52%]

Section 34Point Euclidean spaces[37/73%]

Chapter 14Tensors[146/75%]

Section 35Definition of a tensor. Tensor notation, spatial matrices[39/87%]

Section 36Algebraic operations with tensors[57/74%]

Section 37Tensors in Euclidean space[19/79%]

Section 38Polyvectors and exterior forms[31/58%]