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Curtis M.L. — Abstract Linear Algebra
Curtis M.L. — Abstract Linear Algebra

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Название: Abstract Linear Algebra

Автор: Curtis M.L.

Аннотация:

Beginning from scratch and developing the standard topics of Linear Algebra, this book is intended as a text for a first course on the subject. The goal to which this work leads is the Theorem of Hurwitz - that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. Unique in presenting this material at an elementary level, the book stresses the complete logical development of the subject and will provide a bavuable reference for mathematicians in general.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 168

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_{2}$—space      117
Abelian group      2
Absolute value      6
Adjoint      129
Algebra      18 56
Algebra, alternative      154
Algebra, associative      18 57
Algebra, commutative      57
Algebra, division      155
Algebra, normed      155
Algebraic multiplicity      79 105
Algebraically closed field      4
Annihilator      45
Associator      60 145
Basis      22
Bilinear form      113
Block diagonal matrix      103
Cayley numbers      151
Cayley — Dickson formula      156
Cayley — Dickson process      157
Cayley — Hamilton theorem      84 95
Change-of-basis matrix      53 116
Characteristic of field      4
Characteristic polynomial      83 95
Classical adjoint      71
Coefficients of a polynomial      87
Coefficients of linear system      72
Cofactor      71
column      48
Column spaca      55
Commutator      60 145
Comparable      44
Complementary subspaces      28
complex numbers      6
conjugate      53
Conjugate in normed algebra      145
Conjugate of a matrix      125
Conjugate of complex number      6
Conjugate of quartenion      144
Coordinate vector      51
Coset      32
Curve      133
Curve, differentiable      133
Curve, product      133
Degree of polynomial      7
Determinant      63
Diagonal matrix      14 65
Diagonalizable      104 106
DIMENSION      24 36
Direct sum, external      28
Direct sum, internal      30
Distance      111
Divide      90
Division theorem      88
Divisor of zero      3
Dual basis      42
Dual space      41
Echelon form      69
Eigenspace      39
Eigenvalue      39 76 84
Eigenvector      39
Elementary column operations      70
Elementary matrix      69
Elementary row operations      68
Elimination      73
End(F)      18
Endomorphism      18
EPIC      16
Exact sequence      31
Extension field      4
Exterior algebra on $\mathbb{R}^{3}$      58
Exterior algebra on $\mathbb{R}^{n}$      61
Factor Theorem      89 90
Field      2
Finite set      22
Finite-dimensional      22
Functional      41 120
Fundamental theorem of algebra      4
General linear group      19 65
Generates      12
Geometric multiplicity      39 105
Gram-Schmidt orthnormalization, process      118
Greatest common divisor      90
Group      1
Hamel basis      24
Hermitian form      124
Hermitian inner product      123
Hermitian linear      124
Hermitian matrix      128
Hermitian symmetric      124
Hilbert space      117
Homogeneous system of equations      76
Homomorphism      82
Hurwitz theorem      160
I, j entry      48
Ideal      82
Idempotent      77 97
Idempotent map      20
identity map      15
Identity matrix      52 57
Image      16
Imaginary part      143 145
Indeterminate      87
Infinite set      22
Infinite-dimensional      22
Injective      16
Inner product      111
Inner product space, complex      124
Inner product space, real      116
Integral domain      85
Inverse      52
Irreducible      91
Isomorphism of vector spaces      16
Jacobi identity      60
Join      36
Jordan block      103
Jordan form      104
Kernel      16
Laplace expansion      67
Left multiplication      149
left value      89
Lie algebra      60 131
Lie group      132
Line      36
linear combination      11
Linear geometry of $\mathbb{R}$      36
Linear map      15
Linearly dependent      21
Linearly independent      21
Matrix      14 47
Matrix algebra      58
Matrix multiplication      50
Matrix representation of a bilinear form      115
Matrix representation of a linear map      48
Maximal element      44
Method of elimination      13
Metric      111
Minimal polynomial      92
Monic map      16
Monic polynomial      7 87
Natural map      43
Nilpotent      28 77
Nondegenerate      112
Nonsingular      52
Nonsingular matrix      15
Norm      111 125
Normal matrix      138
Normed algebra      141
Normed vector space      120 125
Oct onions      151
Operator      18
Orthogonal      118 125
Orthogonal complement      122
Orthogonal group      130
Orthogonal map      118
Orthogonal matrix      118 130
Orthonormal      118
Orthonormal basis      118
parallel      36
Parallelogram law      120
Partially ordered set      43
Permutation      6
Plane      36
Point      36
Polar form      120
Polynomial function      87
Positive definite bilinear form      114
Positive definite matrix      128
Preimage      16
Projection      20
Quadratic form      116
Quaternions      144 151
Quotient space      33
Rank      55 115
Rank theorem      25
REAL      9
Real inner product space      116
Real part      143 145
Relatively prime      91
Remainder theorem      90
Ring      81
Ring, associative      81
Ring, commutative      81
Ring, homomorphism      82
Root      4 87
Rotation group      130
Row      48
Row equivalent      68
Row reduced      69
Row space      55
scalar      9
Schwarz inequality      112 115 124
Similar matrices      53
Simply ordered set      44
Singular matrix      15
Skew — Hermitian matrix      128 131
Skew-symmetric matrix      130 131
span      11 12
Special linear group      133
Special orthogonal group      130
Special unitary group      130
Spectral theorem      98 101
Split exact sequence      31
Splitting      31
Square matrix      52 57
Stable subspace      37
Standard basis      23
Subfield      4
Subgroup      5
SubMatrix      56
Subring      82
subspace      11
Sum of subspaces      14
Superdiagonal      101
Surjective      16
Symmetric bilinear form      114
Symmetric matrix      68
Symplectic group      153
Symplectic matrix      153
System of equations      72
Terms of a polynomial      87
Torsion      3
Trace      54
TRANSPOSE      65
Triangle property      111
Triangular matrix      65
Trivial solution      72
UNIT      19 81
Unit element      18 57 81
Unit vector      118
Unitary group      125
Unitary map      125
Unitary matrix      125 130 134
Upper bound      44
Upper triangular      14 65
Value      89
Vector      9
Vector space, over k      10
Zorn’s Lemma      44
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