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Linear algebra
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Mathematics
Area of mathematics
Algebra
OurBigBook.com
Words: 4k
Articles: 132
Table of contents
4k
132
Linear function
Linear algebra
106
Linear map
(linear operator)
Linear algebra
1k
27
Form
(mathematics)
Linear map
12
Linear form
Linear map
362
3
Matrix representation of a linear form
Linear form
36
Dual space
(
V
∗
)
Linear form
302
1
Dual vector
(
e
i
)
Dual space
174
Linear operator
Linear map
85
1
Adjoint operator
(
A
†
)
Linear operator
40
Self-adjoint operator
Linear map
Multilinear map
Linear map
808
18
Bilinear map
Multilinear map
98
Bilinear form
(
B
(
x
,
y
)
)
Multilinear map
294
2
Matrix representation of a bilinear form
Bilinear form
223
1
Effect of a change of basis on the matrix of a bilinear form
(
B
2
=
C
T
BC
)
Matrix representation of a bilinear form
157
Multilinear form
Multilinear map
25
Symmetric bilinear map
Multilinear map
373
9
Symmetric bilinear form
Symmetric bilinear map
76
1
Matrix representation of a symmetric bilinear form
Symmetric bilinear form
71
Hermitian form
Symmetric bilinear map
52
1
Matrix representation of a Hermitian form
Hermitian form
3
Quadratic form
Symmetric bilinear map
181
Positive definite symmetric bilinear form
Symmetric bilinear map
17
1
Matrix representation of a positive definite symmetric bilinear form
Positive definite symmetric bilinear form
6
Skew-symmetric bilinear map
Symmetric bilinear map
8
Skew-symmetric bilinear form
Symmetric bilinear map
5
Symmetric multilinear map
Multilinear map
16
1
Antisymmetric multilinear map
Symmetric multilinear map
8
Alternating multilinear map
Multilinear map
2
Dot product
Linear algebra
177
3
Orthogonality
Dot product
1
Orthonormality
Orthogonality
Angle
Dot product
Cross product
(
x
×
y
)
Linear algebra
1
Jacobi identity
Cross product
Index picking function
Linear algebra
96
3
Kronecker delta
(
δ
ij
)
Index picking function
Levi-Civita symbol
(
ε
)
Index picking function
96
1
Levi-Civita symbol as a tensor
Levi-Civita symbol
70
Projection
(mathematics)
Linear algebra
Matrix
Linear algebra
1k
60
Matrix operation
Matrix
81
6
Determinant
(
d
e
t
)
Matrix operation
23
Matrix inverse
(
M
−
1
)
Matrix operation
38
1
Invertible matrix
Matrix inverse
22
Transpose
(
M
T
)
Matrix operation
20
2
Transpose of a matrix multiplication
Transpose
14
Inverse of the transpose
Transpose
6
Matrix multiplication
Matrix
296
14
System of linear equations
Matrix multiplication
91
4
Application of systems of linear equations
System of linear equations
15
System of linear equations algorithm
System of linear equations
76
2
LINPACK benchmarks
System of linear equations algorithm
Conjugate gradient method
System of linear equations algorithm
76
Application of matrix multiplication
Matrix multiplication
2
Matrix multiplication algorithm
Matrix multiplication
144
6
General matrix matrix multiplication
(GEMM)
Matrix multiplication algorithm
11
1
Strassen algorithm
General matrix matrix multiplication
Multiplication of matrices of specific size
Matrix multiplication algorithm
133
3
Commutative matrix multiplication algorithm
Multiplication of matrices of specific size
94
2x2 matrix multiplication
Multiplication of matrices of specific size
3x3 matrix multiplication
Multiplication of matrices of specific size
Matrix decomposition
Matrix multiplication
Eigenvalues and eigenvectors
Matrix
592
19
Applications of eigenvalues and eigenvectors
Eigenvalues and eigenvectors
Characteristic polynomial
Eigenvalues and eigenvectors
Eigenvalue
Eigenvalues and eigenvectors
56
2
Spectrum
(functional analysis)
Eigenvalue
54
1
Continuous spectrum
(functional analysis)
Spectrum
49
Eigendecomposition of a matrix
Eigenvalues and eigenvectors
494
7
Eigendecomposition of a real symmetric matrix
Eigendecomposition of a matrix
24
Sylvester's law of inertia
Eigendecomposition of a matrix
383
5
Congruent matrix
Sylvester's law of inertia
63
1
Matrix congruence can be seen as the change of basis of a bilinear form
Congruent matrix
41
Matrix similarity
Sylvester's law of inertia
Metric signature
Sylvester's law of inertia
1
Metric signature matrix
Metric signature
Eigenvector
Eigenvalues and eigenvectors
2
Eigenvectors and eigenvalues of the identity matrix
Eigenvalues and eigenvectors
Spectral theorem
Eigenvalues and eigenvectors
40
3
Hermitian matrix
(complex analogue of symmetric matrix)
Spectral theorem
40
2
Hermitian operator
Hermitian matrix
40
1
Riesz representation theorem
Hermitian operator
Kronecker product
Matrix
Named matrix
Matrix
207
16
Dense and sparse matrices
Named matrix
80
2
Dense matrix
Dense and sparse matrices
Sparse matrix
Dense and sparse matrices
Diagonal matrix
Named matrix
10
2
Scalar matrix
(
Z
(
V
)
)
Diagonal matrix
5
1
Identity matrix
(
I
n
)
Scalar matrix
Square matrix
Named matrix
28
1
Matrix ring
(Matrix ring of degree n,
M
n
, Set of all n-by-y square matrices)
Square matrix
28
Orthogonal matrix
Named matrix
23
1
Unitary matrix
Orthogonal matrix
19
Triangular matrix
Named matrix
Symmetric matrix
Named matrix
66
4
Definite matrix
Symmetric matrix
27
1
Positive definite matrix
Definite matrix
18
Skew-symmetric matrix
(Antisymmetric matrix)
Symmetric matrix
21
1
Skew-symmetric form
Skew-symmetric matrix
Vector space
Linear algebra
300
10
Basis
(linear algebra)
Vector space
199
4
Change of basis
Basis
199
2
Change of basis matrix
Change of basis
152
Change of basis between symmetric matrices
Change of basis
23
Linear independence
Basis
Classification of vector spaces
Vector space
Underlying field of a vector space
Vector space
74
Tensor product
(
⊗
)
Vector space
Vector
(mathematics)
Vector space
27
1
Scalar
(mathematics)
Vector
27
Tensor
Linear algebra
697
17
A linear map is a (1,1) tensor
Tensor
51
Tensor space
(
T
(
m
,
n
)
)
Tensor
7
1
Order of a tensor
Tensor space
6
Einstein notation
(Einstein summation convention)
Tensor
561
13
Raised and lowered indices
Einstein notation
72
3
Raised index
Raised and lowered indices
Lowered index
Raised and lowered indices
Raising and lowering indices
Raised and lowered indices
Implicit metric signature in Einstein notation
Einstein notation
57
Einstein notation for partial derivatives
Einstein notation
351
4
Divergence in Einstein notation
(
∂
i
)
Einstein notation for partial derivatives
97
Laplacian in Einstein notation
(
∂
i
∂
i
)
Einstein notation for partial derivatives
187
2
d'Alembert operator in Einstein notation
(
∂
i
∂
i
)
Laplacian in Einstein notation
88
1
Klein-Gordon equation in Einstein notation
d'Alembert operator in Einstein notation
30
Covariance and contravariance of vectors
Einstein notation
2
Covariant vector
Covariance and contravariance of vectors
Contravariant vector
Covariance and contravariance of vectors
Linear algebra bibliography
Linear algebra
5
1
Interactive Linear Algebra by Margalit and Rabinoff
Linear algebra bibliography
5
Ancestors
(4)
Algebra
Area of mathematics
Mathematics
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