Part II

Linear Algebra and Geometry

[625/61%]

Chapter VIIVector spaces[62/85%]

Section 34Concept of a vector space. Bases[14/79%]

Section 35Subspaces[27/78%]

Section 36Linear functions and mappings[21/100%]

Chapter VIIIBilinear and quadratic functions[81/63%]

Section 37General bilinear and sesquilinear functions[46/63%]

Section 38Symmetric bilinear, Hermitian and quadratic functions[35/63%]

Chapter IXLinear operators[149/56%]

Section 39Definition of a linear operator. The image, the kernel, the matrix of a linear operator[24/58%]

Section 40Eigenvectors, invariant subspaces, root subspaces[44/66%]

Section 41Jordan canonical form and its applications. Minimal polynomial[47/66%]

Section 42Normed vector spaces and algebras. Non-negative matrices[34/29%]

Chapter XMetric vector spaces[135/53%]

Section 43Geometry of metric spaces[49/41%]

Section 44Adjoint and normal operators[32/63%]

Section 45Selfadjoint operators. Reduction of quadratic functions to principal axes[21/48%]

Section 46Orthogonal and unitary operators. Polar factorization[33/64%]

Chapter XITensors[37/65%]

Section 47Basic concepts[19/89%]

Section 48Symmetric and skew-symmetric tensors[18/39%]

Chapter XIIAffine, Euclidean, and projective geometry[161/61%]

Section 49Affine spaces[38/47%]

Section 50Convex sets[37/62%]

Section 51Euclidean spaces[24/71%]

Section 52Hypersurfaces of second degree[28/93%]

Section 53Projective spaces[34/44%]