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Dieudonne J. — Linear Algebra and Geometry.
Dieudonne J. — Linear Algebra and Geometry.

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Название: Linear Algebra and Geometry.

Автор: Dieudonne J.


This book gives a complete and detailed account of the basic ideas and theorems of elementary linear algebra which represent the very least a competent French "bachelier" should know when embarking upon the "propedeutique" courses. The general approach and content of the book were determined by the desire to prepare the student to assimilate as easily as possible, the actual teaching he is receiving at this time, which he should, in turn, regard as a natural extension of the work he has already been doing. At the moment, it is unlikely that one in a thousand students could cope with this book, unaided and without considerable hard work. This state of affairs says a great deal about the lack of cohesion in our teaching programmes. For years, teachers everywhere have expressed their concern about the everidening gap between the methods and attitudes to the teaching of Mathematics in the secondary schools on the one hand and in the universities on the other. Having participated in many discussions on this problem, I have succeeded in convincing myself that even among those secondary school teachers who are most keenly aware of the need for reform, there exists a great uncertainty about the content of new courses, their structure and their connection with the various courses in the university. So it is, in fact, for these people that this book is primarily intended. I have devised it as a "teacher's book"; in other words, its aim is to provide a solid framework upon which to base lively oral teaching adapted to those pupils for whom it is intended.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 205

Добавлена в каталог: 17.02.2013

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Предметный указатель
Multiplication by a scalar      30
Multiplicative group of real numbers $\neq 0$      1.5
Multiplicator of a line similitude      5.1.12 Ap. no.
Multiplicator of an affine similitude      5.1.14
Negative acute/obtuse angle
Negative definite non-degenerate form      Ap. II no.
Negative of a real number      1.4
Negative pair      4.3.1
Negative real number      1.17
Negative right angle      5.4.3
Negative triple      6.2.12
Nilpotent endomorphism      4.1 Ex.
Non-Euclidean space      Ap. II no.
Norm of a Euclidean space      5.1.1
Norm of a quaternion      Ap. IV no.
Normal endomorphism      5.3 Ex. 7.2 Ex. Ap. no.
Normal hyperplane to a non-Euclidean line      Ap. II no. 27
Normal line to a hyperplane      Ap. II no. 27
Normal line to a sphere      Ap. III no.
Normalizer of a subgroup      4.1 Ex.
Null element      3.1.1
Null space of a linear transformation      3.2.3
Obtuse positive/negative angle      5.4.12
Obtuse sector      5.4.13
Open ball      5.1.9
Open half-line      3.3.3
Open half-space      3.3.7
Open sector      4.3.5
Open segment      3.3.4
Operator      3.2.1
Opposed half-lines      3.3.3
Opposite of a vector      3.1.5
Orientated vector space      4.3.1 6.2.12
Orientation      3.3.3 4.3.1 6.2.12
Orientation, (direct sum of orientations), (supplementary orientation)      6.2.14
Origin of a half-line      3.3.3
Origin of a segment      3.3.4
Origin of a vector space      4.3.1 6.2.12
Orthogonal basis      5.2.1 7.1.1 Ap. no.
Orthogonal group      5.1.12 Ap. no.
Orthogonal hyperplane to a line      5.1.7 Ap. no.
Orthogonal line to a hyperplane      5.1.7 Ap. no.
Orthogonal matrix      5.2.6 7.1.5
Orthogonal of a subspace of E in E*      Ap. II no.
Orthogonal projection      5.1.6 5.1.8
Orthogonal sets      5.1.6
Orthogonal subspace to another subspace (relative to $\Phi$)      Ap. II no.
Orthogonal symmetry      5.1.13 5.1.15
Orthogonal transformation      5.1.12 Ap. no.
Orthogonal vectors      5.1.4 Ap. no.
Orthonormalization      5.2 Ex.
p-Linear map      3.2.15
Parallel (Clifford parallel)      Ap. IV no.
Parallel half-lines      3.3.3
Parallel linear varieties      3.1.13
Parallelogram      3.3 Ex.
Parametric representation of a line      3.3.1
Paratactic circles      Ap. IV no.
Part (pure part, scalar part of a quaternion)      Ap. IV no.
Passing through a point (linear variety passing through a point)      3.1.10
Permutation matrix      6.1 Ex.
Perpendicular concurrent non-Euclidean lines      Ap. II no. 27
Perpendicular line and hyperplane      5.1.8 Ap. no. 27
Plane (affine plane)      6.1.5
Plane (Euclidean plane)      2.1
Plane (hyperbolic plane)      Ap. II no.
Plane (projective plane)      Ap. II no.
Plane (vector plane)      4.3.1
Point of a projective space      Ap. II no.
Point of a vector space      3.0
Points conjugate with respect to a projective quadric      Ap. II no.
Points on the same side/opposite side/strictly on the same side/strictly one each side of a hyperplane      3.3.7
Polar hyperplane of a point      Ap. II no.
Pole of a projective hyperplane      Ap. II no.
Pole of an inversion      Ap. III no.
Polynomial (characteristic polynomial of an endomorphism)      4.2.14 6.2.10
Positive acute/obtuse angle      5.4.12
Positive definite form      50 Ap. no.
Positive pair of vectors/half-lines      6.2.12
Positive real number      1.17
Positive right angle      5.4.3
Positive self-adjoint endomorphism      5.2 Ex. 7.2 Ex.
Positive triple of vectors/half-lines      6.2.12
Power of a point with respect to a sphere      5.1 Ex.
Power of an inversion      Ap. III no.
Product (inner product of two vectors)      5.10
Product (vector product of two vectors)      7.1.7
Product by a scalar      30
Product of additive subgroups of End(E)      4.1 Ex.
Product of matrices      4.1.12 6.1.8
Product vector space      3.1.8
Projection (orthogonal projection)      5.1.6 5.1.8
Projection (stereographic projection)      5.4.10 Ap. no.
Projection relative to a direct decomposition/parallel to a subspace of a vector space      3.2.2
Projective frame of reference      6.1 Ex.
Projective group      Ap. II no.
Projective hyperplane      Ap. II no.
Projective line      Ap. II no.
Projective linear mapping      Ap. II no.
Projective linear variety      Ap. II no.
Projective plane      Ap. II no.
Projective quadric      Ap. II no.
Projective space      Ap. II no.
Projectivity      Ap. II no.
Pure part of a quaternion      Ap. IV no.
Pure quaternion      Ap. IV no.
Pythagoras' theorem      5.1.5
Quadratic map      3.2 Ex.
Quadric (affine quadric)      Ap. II no.
Quadric (projective quadric)      Ap. II no.
Quasi-symmetry      4.1 Ex.
Quaternion (conjugate quaternion)      Ap. IV no.
Quaternion (pure quaternion)      Ap. IV no.
Quaternion field      Ap. IV no.
Radical hyperplane      5.1 Ex.
Radius of a ball/sphere      5.1.9
Rank of a bilinear form      Ap. II no.
Rank of a linear map      4.1.1 6.1.6 Ap. no.
Rank of a matrix      4.1.11 6.1.8
Real part of a complex number      5.3.3
Real vector space      30
Relation (Grassmann's relation)      Ap. II no.
Relation (order relation on set of angles $\neq\widetilde{\omega}$)
Relation (total ordering relation)      1.11
Representation (Cayley's relation)      5.5 Ex. 7.2 Ex.
Representation (parametric relation of a line)      3.3.1
Right angle (positive/negative right angle for half-lines)      5.4.3
Right angle for half-lines      5.4.2
Right angle for lines      5.4.14
Right angled sector      5.4.13
Rotation      5.3.1 7.2.1 Ap. no.
Rotation of angle $\theta$      5.4.1
Rule of signs      1.23
scalar      30
Scalar matrix      4.1.13 6.1.8
Scalar part of a quaternion      Ap. IV no.
Sector (acute, obtuse, right-angled sector)      5.4.13
Sector (closed major/minor/straight sector)      4.3.8
Sector (closed/open sector, sector closed at a open at b)      3.3.4
Sector (open major/minor/straight sector)      4.3.5
Self-adjoint endomorphism      5.2.7 7.1.5 Ap. no.
Sign of a real number      1.27
Signature of a symmetric bilinear form      4.1 Ex. Ap. no.
Similitude (affine similitude)      5.1.14
Similitude (direct similitude)      5.3.1 5.3.4 7.2.1 7.2.6 Ap. no.
Similitude (inverse similitude)      5.3.1 5.3.4 7.2.1 7.2.6 Ap. no.
Similitude (linear similitude)      5.1.12 Ap. no.
Sine of an angle      5.4.3
Space (Euclidean space)      50
Space (n-dimensional Euclidean space)      Ap. II no.
Space (non-Euclidean space)      Ap. II no. 27
Space (projective space)      Ap. II no.
Space (real vector space)      30
Space (three-dimensional space)      6.1.4
Space (two-dimensional space)      4.1.5
Space (vector space obtained by taking a point as origin)      3.2.21
Sphere (degenerate sphere)      Ap. III no.
Sphere of an inversion      Ap. III no.
Sphere, unit sphere      5.1.9
Spheres (concentric spheres)      5.1.9
Spheres (coorthogonal spheres)      5.1 Ex. Ap. no.
Spheres (tangential spheres)      5.1.11
Square root      1.31
Stationary values of an endomorphism      5.2 Ex. 7.1 Ex.
Stereographic projection      5.4.10 Ap. no.
Straight angle      5.4.1
Straight sector      4.3.5 4.3.8
Strictly greater than/less than      1.17
Strictly one on each side/on the same side of a hyperplane      3.3.7
Strictly positive/negative      1.17
Structure (induced structure)      2.4
Structure of a Euclidean space      50
Subgroup (maximal subgroup)      4.1 Ex.
subspace      3.1.6
Subspace (characteristic subspace of an endomorphism)      3.2.10
Subspace (isotropic subspace, totally isotropic subspace)      Ap. II no.
Subspace of E* orthogonal to a subspace of E      Ap. II no.
Subspaces (supplementary subspaces)      3.1.8
Sum (direct sum of two orientations      6.2.14
Sum (direct sum of two subspaces)      3.1.8
Sum of subspaces      3.1.7
Supplementary orientations      6.2.14
Supplementary subspaces      3.1.8
Sylvester's law of inertia      Ap. II no.
Symmetric (positive symmetric matrix)      5.2 Ex. 7.1 Ex.
Symmetric bilinear map      3.2.14
Symmetric endomorphism      5.2.5 7.1.5 Ap. no.
Symmetric matrix      4.2.4 6.2.3
Symmetric trilinear mapping      3.2.15
Symmetry (orthogonal symmetry)      5.1.13 5.1.15
Symmetry about the origin      3.2.11
Symmetry in a sphere      Ap. III no.
Tangent of an angle made by half-lines      5.4.5
Tangent of an angle made by lines      5.4.14
Tangential linear variety to a sphere      5.1.10
Tangential projective linear variety to a quadric      Ap. II no.
Tangential spheres      5.1.11
Theorem (Cayley — Hamilton theorem)      4.1 Ex. 6.2 Ex.
Theorem (Fundamental theorem of affine geometry)      4.1 Ex.
Theorem (Pythagoras' theorem)      5.1.5
Total ordering relation      1.11
Totally isotropic subspace      Ap. II no.
Totally ordered subset      1.11
Totally orthogonal subspace      Ap. II no.
Trace of a quaternion      Ap. IV no.
Trace of an endomorphism/matrix      4.2 Ex. 6.2 Ex.
Transformation (orthogonal transformation)      5.1.12 Ap. no.
Transitive (triply transformation group)      4.1 Ex.
Translation (Clifford translation)      Ap. IV no.
Translation associated with an affine map      3.2.17
Translation by the vector a      3.1.9
Transpose of a linear mapping      Ap. II no.
Transpose of a matrix      4.2.4 6.2.3
Transvection      3.3 Ex.
Triangular (upper triangular matrix)      4.2.14 6.2.10
Triangular inequality      5.1.3
Trilinear map      3.2.15
Triple (direct/indirect/positive/negative triple)      6.2.12
Unimodular group      4.2 Ex. 6.2 Ex.
Unit ball/sphere      5.1.9
Unit element      1.8
Unit element of the ring End(E)      3.2.8
Unit sphere      5.1.9
Unit vector      5.1.1
Value (absolute value of a complex number)      5.5.4
Value (absolute value of a real number)      1.19
Value (characteristic value of an endomorphism)      3.2.10
Value (stationary value of an endomorphism)      5.2 Ex. 7.1 Ex.
Varieties (parallel linear varieties)      3.1.13
Variety (affine linear variety)      3.1.10
Variety (coordinate variety)      3.1.14
Variety (linear variety tangential to a sphere)      5.1.10
Variety (projective linear variety tangential to a quadric)      Ap. II no.
Variety (projective linear variety)      Ap. II no.
Vector      30
Vector (direction vector a line)      3.3.1
Vector (direction vector of a half-line)      3.3.3
Vector (isotropic vector)      Ap. II no.
Vector (unit vector)      5.1.1
Vector hyperplane      3.3.5
Vector line      3.3.1
Vector plane      3.1.6
Vector product      7.1.7
Vector space      30
Vectors (linearly dependent/independent vectors)      4.1.1
Vectors (orthogonal vectors)      5.1.4 Ap. no.
Vertex of a sector      4.3.5 4.3.8
Vertex of a stereographic projection      Ap. III no.
Zero      1.3 3.1.1
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