Lin I.H. — Geometric Linear Algebra. Vol. 1 :: Электронная библиотека попечительского совета мехмата МГУ

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Lin I.H. — Geometric Linear Algebra. Vol. 1

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Название: Geometric Linear Algebra. Vol. 1

Автор: Lin I.H.

Аннотация:

Writing for freshmen and sophomores in college or advanced high school students, Lin (National Taiwan Normal U.) takes the view that recently geometric linear algebra has become too algebraic and tackles the subject from another angle, starting with the affine and linear structures of real vector spaces R1, R2 and R3, stepping through them as one-dimensional (including affine variants), two- dimensional (including linear transformations and affine transformations) and three dimensions, including lines and planes in space. In appendices Lin gives the background information necessary to follow the text and do the exercises, including an extended description of algebraic linear algebra.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 856

Добавлена в каталог: 04.07.2008

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Предметный указатель

Row-reduced echelon matrix      164 443 464 721
Row-reduced echelon matrix, concrete examples      150 442
Row-reduced echelon matrix, implications and applications      722—727
Schur's formula      182; see “Block matrix”
Set      681
Set, cartesian product      681
Set, difference      681
Set, empty set      681
Set, intersection      681
Set, member element      681
Set, subset, proper subset      681
Set, union      681
shearing      100 265 392 612; transformation”
Signed length (of a segment)      6
simplex      642 654 662
Simplex, 0-simplex, i.e. a point      5
Simplex, 1-simplex, i.e. a line segment      5 18
Simplex, 2-simplex, usually called a triangle in $\mathbb{R}^2$       65; see “Triangle”
Simplex, 3-simplex, usually called a tetrahedron in $\mathbb{R}^3$       see “Tetrahedron”
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ )      590 642 654 662
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), barycentric subdivision      666
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), boundary, interior, exterior      662
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), edge      642
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), face      642
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), generalized Euler formula      667
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), k-dimensional volume      641
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), open simplex      654
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), separation      663
Simplex, k-simplex or k-tetrahedron (in $\mathbb{R}^\mathrm{n}$ ), vertex      642
Simultaneously, diagonalizable      209 213
Simultaneously, lower or upper triangularizable      215
Singular matrix      see “Matrix”
Singular value (of a matrix)      177 771
Singular value (of a matrix), decomposition theorem (SVD)      178 771
Singular value (of a matrix), generalized inverse      176 776;
Singular value (of a matrix), polar decomposition      772; see “the index”
Standard basis or natural basis      see “Basis”
Standard inner product or natural inner product for $\mathbb{R}^\mathrm{n}$ or $\mathbb{C}^\mathrm{n}$       773; see “Inner product”
Standard n-dimensional vector space $\mathbb{R}^\mathrm{n}$ or $\mathbb{C}^\mathrm{n}$ or $\mathbb{F}^\mathrm{n}$       693 698
Standard one-dimensional vector space $\mathbb{R}$       12
Standard three-dimensional vector space $\mathbb{R}^3$       327
Standard two-dimensional vector space $\mathbb{R}^2$       37
Standard zero-dimensional vector space $\{ \vec{0} \}$       694 698
Stretch or stretching      see “Affine transformation”
Sylverster's law of inertia (of a symmetric matrix)      166 454 467 470 471
Sylverster's law of inertia (of a symmetric matrix) index      166 454 467 470 471
Sylverster's law of inertia (of a symmetric matrix) rank      166 454 467 470 471
Sylverster's law of inertia (of a symmetric matrix) signature      166 454 467 470 471
Tensor product (of two matrices)      148
Tetrahedron in $\mathbb{R}^3$       356 363 401 638 642;
Tetrahedron in $\mathbb{R}^3$ edge      356
Tetrahedron in $\mathbb{R}^3$ face      356
Tetrahedron in $\mathbb{R}^3$ median plane      356
Tetrahedron in $\mathbb{R}^3$ vertex      356
Transition matrix between bases      see “Change of coordinates”
Transition matrix in Markov chain      see “Markov chain”
Translation      see “Affine transformation”
TRANSPOSE      see “Matrix”
Triangle in $\mathbb{R}^2$       65; see “Simplex”
Triangle in $\mathbb{R}^2$ centroid      65
Triangle in $\mathbb{R}^2$ median      65
Triangle in $\mathbb{R}^2$ side      65
Triangle in $\mathbb{R}^2$ vertex      65
Unitary matrix      782 783 786; adjoint
Unitary matrix, unitarily similar      786

Upper triangular matrix      161 701;
Vandermonde determinant      750
Vector in abstract sense      692
Vector in abstract sense, addition      692
Vector in abstract sense, linear combination: coefficient      695
Vector in abstract sense, linear dependence      696
Vector in abstract sense, linear independence      696
Vector in abstract sense, negative or inverse of a vector      692
Vector in abstract sense, nonnegative vector      503
Vector in abstract sense, positive vector      503
Vector in abstract sense, scalar multiplication      692
Vector in abstract sense, scalar multiplication, product      692
Vector in abstract sense, scalar multiplication, scalar      684 692
Vector in abstract sense, sum      692
Vector in abstract sense, zero vector      692
Vector or linear space in abstract sense      691
Vector or linear space in abstract sense, basis, basis vectors      697; see “Basis”
Vector or linear space in abstract sense, complex vector space      29 692
Vector or linear space in abstract sense, dimension      698
Vector or linear space in abstract sense, dimension, finite-dimensional, n-dimensional      697 698
Vector or linear space in abstract sense, dimension, infinite-dimensional      697
Vector or linear space in abstract sense, ordered basis      698
Vector or linear space in abstract sense, quotient space      695
Vector or linear space in abstract sense, real vector space      29 692
Vector or linear space in abstract sense, Steinitz's replacement theorem      697
Vector or linear space in abstract sense, subspace      694; see “Linear or vector subspace”
Vector or linear space, one-dimensional real vector space $\mathbb{R}$       8 12 13 41
Vector or linear space, three-dimensional real vector space $\mathbb{R}^3$       324 326 327
Vector or linear space, two-dimensional real vector space $\mathbb{R}^2$       28 31 34 37 41
Vector, line vector      7
Vector, line vector, identical vectors      7
Vector, line vector, identical vectors, parallel invariance of vectors      7
Vector, line vector, linear dependence      9
Vector, line vector, linear independence      1
Vector, line vector, scalar multiplication (product)      8 9
Vector, line vector, zero vector      7
Vector, plane vector      24
Vector, plane vector, addition (sum) of vectors      26
Vector, plane vector, identical vectors      25
Vector, plane vector, identical vectors, parallelogram law or parallel invariance      25
Vector, plane vector, linear combination: coefficient      31
Vector, plane vector, linear dependence      32 40
Vector, plane vector, linear independence      33 41
Vector, plane vector, negative of a vector      26
Vector, plane vector, scalar      28
Vector, plane vector, scalar multiplication      27
Vector, plane vector, subtraction vector      27
Vector, plane vector, zero vector      24 27
Vector, spatial vector      29 320
Vectorized space or vectorization of a line      9
Vectorized space or vectorization of a line, base vector      9
Vectorized space or vectorization of a line, position vector      7 8
Vectorized space or vectorization of a line, scalar product      9
Vectorized space or vectorization of a line, zero vector      9
Vectorized space or vectorization of a plane      30 31
Vectorized space or vectorization of a plane, addition      30
Vectorized space or vectorization of a plane, basis, basis vector      31
Vectorized space or vectorization of a plane, position vector      30
Vectorized space or vectorization of a plane, scalar multiplication      30
Vectorized space or vectorization of a plane, zero vector      31
Vectorized space or vectorization of a space      323
Vectorized space or vectorization of a space, basis, basis vector      324
Vectorized space or vectorization of a space, origin      324
Vectorized space or vectorization of a space, position vector      324
Vectorized space or vectorization of a space, zero vector      324

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