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Blyth T.S., Robertson E.F. — Further Linear Algebra
Blyth T.S., Robertson E.F. — Further Linear Algebra

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Название: Further Linear Algebra

Авторы: Blyth T.S., Robertson E.F.

Аннотация:

Further Linear Algebra is a natural sequel to the authors' highly acclaimed SUMS volume "Basic Linear Algebra". The more advanced topics covered here take the reader to the very heart of the subject, and include inner product spaces, direct sums of subspaces, the primary decomposition theorem and various canonical forms for matrices. Furthermore, the authors provide a brief introduction to the use of MAPLE in linear algebra calculations, and biographical profiles of eminent mathematicians associated with the subject.
An introductory chapter recaps the prerequisites (for those readers unfamiliar with the first volume), and a wide range of worked examples and exercises (with solutions) are strategically placed throughout the text to consolidate understanding.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2002

Количество страниц: 230

Добавлена в каталог: 04.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_2$ space      14
Adjoint of mapping      104
Adjoint of matrix      109
Algebra      6
Algebraic multiplicity      8
angle      21
Annihilated by vector      100
Annihilator      77 100
Associated quadratic form      132
Basis      3
bessel      172
Bessel’s inequality      17
bezout      173
Bidual      96
Biiranspose      99
Bilinear form      127
Block diagonal      39
Canonical form      8 109
Canonical isomorphism      102
Canonical mapping      96
Cauchy      174
Cauchy — Schwarz inequality      13
Cayley      175
Cayley — Hamilton theorem      10
Centro-symmetric      28
Change of Basis Theorem      7
Characteristic equation      8
Characteristic polynomial      8
Classical canonical matrix      87
Classical p-matrix      87
Column rank      6
Companion matrix      79
Complex inner product space      11
Complex vector space      2
Congruent matrices      130
Conjugate isomorphism      103
Conjugate transformation      103
Conjugate transpose      109
Coordinate form      92
Cyclic basis      79
Cyclic subspace      79
Cyclic vector      79
Determinant      8
Diagonal matrix      8
Diagonalisable      44
Diagonalisable mapping      9
Diagonalisable matrix      9
DIMENSION      3
Dimension Theorem      4
Direct sum      25
Distance      13
Dot product      12
Dual basis      92
Dual space      90
Eigenspace      9
Eigenvalue of mapping      9
Eigenvalue of matrix      8
Eigenvector      8
Elementary divisors      82
Elementary Jordan matrix      59
Elementary matrix      6
Equal matrices      5
Even mapping      26
f-annihilator      77
f-cyclic subspace      79
f-invariant      37
f-stable      37
F-vector space      2
fibonacci      176
Finite-dimensional      3
FOURIER      178
Fourier coefficients      20
Fourier expansion      20
Fourier series representation      33
Geometric multiplicity      9
Gram      179
Gram matrix      126
Gram — Schmidt process      18
Hamilton      180
hermite      182
hilbert      183
Hilbert space      14
Idempotent      29
Identity matrix      5
Image      4
Induced mapping      76
Inner product      11
Inner product isomorphism      22
Inner product space      11
Invariant      37
Inverse      6
Invertible      6
Isomorphism      4
JORDAN      184
Jordan Basis      66
Jordan block matrix      59
Jordan decomposition      53
Jordan Form Theorem      62
Jordan Matrix      63
Jordan normal form      63
Kernel      4
kronecker      185
Lagrange      186
Lagrange polynomials      93
Laplace      188
Left inverse      6
Lie      189
linear combination      2
Linear differential equations      70
Linear form      90
Linear functional      90
Linear mapping      3
Linearly dependent      3
Linearly independent      3
Maple      153
Matrix      4
Matrix of a linear mapping      5
Matrix of bilinear form      128
Matrix of real quadratic form      132
Matrix product      5
Minimum polynomial      10
Nilpotent index      57
Nilpotent mapping      47
Nilpotent matrix      47
Norm      13
Normal mapping      105 116
Normal matrix      116
Normalising an element      16
Nullity      4
Odd mapping      26
Ordered basis      5
Ortho-diagonalisable      113
Ortho-projection      110
Orthogonal      7 15 109
Orthogonal complement      33
Orthogonal direct sum      110
Orthogonal subset      15
Orthogonally similar      109
Orthonormal basis      17
Orthonormal subset      15
Parallelogram identity      15
Parseval      190
Parseval’s identity      20
Positive definite mapping      123
Positive definite matrix      126
Positive definite quadratic form      138
Positive mapping      123
Positive matrix      126
Primary decomposition theorem      40
Product of matrices      6
Projection      29
Projection on A parallel to B      29
Quadratic form      131
Quotient space      73
Rank      4 6
Rank of quadratic form      135
Rational canonical matrix      83
Real inner product space      11
Real vector space      2
Right inverse      6
Rotation      152
Row rank      6
Scalar product      12
Schmidt      191
Schwarz      193
Self-adjoint      111
Self-adjoint mapping      105
Signature of quadratic form      135
Similar      8
Skew-adjoint mapping      142
Skew-symmetric form      131
Skew-symmetric matrix      142
Spanning set      3
Spectral resolution      115
Square summable      14
Stable      37
Standard inner product      12
subspace      2
Subspace spanned by S      3
Sum of subspaces      24
Sylvester      194
Symmetric form      131
System of differential equations      70
toeplitz      195
Trace      12
Transition matrix      7
Transpose of a mapping      98
Transpose of a matrix      5
Triangle inequality      13
Triangular Form Theorem      50
Triangular mapping      47
Triangular matrix      47
Unitarily similar      109
Unitary      109
Vandermonde      196
Vandermonde matrix      93
Vector space      2
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