# Linear algebra: Trending topics

The following are the current most viewed articles on Wikipedia within Wikipedia's Linear algebra category. Think of it as a What's Hot list for Linear algebra. More info »

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Rank Topic Wikipedia views
1 Matrix (mathematics) 7,196
2 Eigenvalue, eigenvector and eigenspace 5,471
3 Dimension 5,436
4 Dot product 5,112
5 Determinant 5,078
6 Invertible matrix 3,188
7 Euclidean vector 2,976
8 Linear algebra 2,682
9 Vector space 2,674
10 System of linear equations 2,317
11 Singular value decomposition 2,301
12 Orthogonality 2,097
13 Transpose 2,001
14 Norm (mathematics) 1,875
15 Transformation matrix 1,691
16 Trace (linear algebra) 1,649
17 Euclidean space 1,620
18 Rank (linear algebra) 1,600
19 Hilbert space 1,582
20 Unit vector 1,544
21 Linear map 1,480
22 Cramer's rule 1,410
23 Linear independence 1,241
24 Cauchy–Schwarz inequality 1,224
25 Basis (linear algebra) 1,182
26 Projection (linear algebra) 1,091
27 Affine transformation 1,071
28 Triangle inequality 1,048
29 3D projection 967
30 Kernel (matrix) 901
31 Matrix norm 889
32 Identity matrix 888
33 Bra-ket notation 830
34 Matrix calculus 731
35 Line segment 686
36 Conjugate transpose 657
37 Gram–Schmidt process 622
38 Linear combination 619
39 Column space 605
41 Levi-Civita symbol 574
42 Permanent 573
43 Linear subspace 565
44 Linear span 557
46 Eigendecomposition of a matrix 479
47 Hyperplane 470
48 Spectral theorem 455
49 Characteristic polynomial 454
50 Dual space 448
51 Jordan normal form 446
52 Orthonormal basis 441
53 Elementary matrix 431
54 Scalar (mathematics) 413
55 Homogeneous coordinates 403
56 Homogeneous function 376
57 Dimension (vector space) 373
58 Affine space 363
59 Orthonormality 338
60 Cayley–Hamilton theorem 331
61 Cofactor (linear algebra) 304
62 Barycentric coordinate system (mathematics) 301
63 Tikhonov regularization 298
64 Compressed sensing 284
65 General linear group 281
66 Vector-valued function 279
67 Row and column spaces 261
69 Non-negative matrix factorization 258
70 Row space 240
71 Pseudovector 238
72 Examples of vector spaces 231
73 Linear functional 230
74 Kernel (algebra) 222
75 Change of basis 221
76 Euclidean subspace 218
77 Overdetermined system 217
78 Line-line intersection 208
79 Toeplitz matrix 205
80 Spectral theory 202
81 Woodbury matrix identity 192
82 Rank–nullity theorem 169
83 Schur complement 163
84 Column vector 162
85 Null vector 160
86 Coordinate vector 159
87 Shear mapping 155
88 List of linear algebra topics 139
89 Rule of Sarrus 134
90 Basis function 131
91 Sherman–Morrison formula 131
92 Shear matrix 130
93 Standard basis 123
94 Direct sum of modules 122
95 Newton's identities 119
96 Row vector 117
97 Generalized eigenvector 117
98 Split-complex number 115
99 Orthogonal complement 115
100 Seven-dimensional cross product 115
101 Special linear group 113
102 Unitary transformation 113
103 Fundamental theorem of linear algebra 113
104 Invariants of tensors 113
105 Orientation (mathematics) 109
106 Scalar multiplication 107
107 Kernel (linear operator) 107
108 Dual number 106
109 Invariant subspace 106
110 Leibniz formula for determinants 104
111 Quotient space (linear algebra) 101
112 Rayleigh quotient 96
113 Direction vector 96
114 Orthogonalization 93
115 Pairing 91
116 Linear inequality 83
117 Symplectic vector space 80
118 2 × 2 real matrices 79
119 Pseudoscalar 78
120 Rotation operator (vector space) 78
121 Codimension 76
122 Gershgorin circle theorem 76
123 Matrix determinant lemma 76
124 Numerical methods for linear least squares 75
125 Polarization identity 75
126 Row equivalence 73
127 Coefficient matrix 72
128 Sesquilinear form 71
129 Fredholm alternative 71
130 Reduction (mathematics) 69
131 Vectorization (mathematics) 68
132 Orthant 66
133 Dimension theorem for vector spaces 63
134 Orthographic projection (geometry) 60
135 Binomial inverse theorem 59
136 Coordinate space 57
137 Dual basis 56
138 Bidiagonal matrix 52
139 Schmidt decomposition 51
140 Sylvester's law of inertia 49
142 Delta operator 47
143 Jordan–Chevalley decomposition 47
144 Frame of a vector space 47
145 Complex conjugate vector space 46
146 Linear complementarity problem 46
147 Sylvester's determinant theorem 46
148 Principal axis theorem 46
149 Partial trace 45
150 Conformable matrix 43
151 Trilinear coordinates 42
152 Squeeze mapping 41
153 Polynomial basis 39
154 Immanant of a matrix 38
156 Sublinear function 35
157 Dual norm 35
159 Frobenius normal form 32
160 Antilinear map 31
161 Generalizations of Pauli matrices 31
162 Majorization 30
163 Defective matrix 30
164 Eigenvalue perturbation 30
165 Orthogonal Procrustes problem 29
166 Linear complex structure 28
167 Matrix congruence 28
168 Flat (geometry) 28
169 Choi's theorem on completely positive maps 27
170 Nonlinear eigenproblem 27
171 Flag (linear algebra) 26
172 Balanced set 26
173 Inverse eigenvalues theorem 26
174 Matrix pencil 25
175 Resolvent set 25
176 Antiunitary operator 23
177 Stabilizer code 23
178 Independent equation 23
179 Centrosymmetric matrix 23
180 Golden–Thompson inequality 23
181 Restricted isometry property 23
183 Christoffel–Darboux formula 23
184 Projection-valued measure 22
185 Indeterminate system 22
186 Steinitz exchange lemma 22
187 Category of vector spaces 21
188 Hilbert–Poincaré series 21
189 Big M method 21
190 Rouché–Capelli theorem 20
191 Overcompleteness 19
192 Generalized singular value decomposition 18
193 Hamming space 18
194 Commutation matrix 18
195 Controlled invariant subspace 18
196 Quaternionic matrix 17
197 Relative dimension 17
198 Orthogonal diagonalization 17
199 Entanglement-assisted stabilizer formalism 17
200 Canonical basis 16
201 Spinors in three dimensions 16
202 Eigenplane 15
203 Change of bases 15
204 Peetre's inequality 15
205 Semi-simple operator 15
206 Asymmetric norm 15
207 Zero mode 15
208 Zech's logarithms 14
209 Lattice reduction 14
210 Weyl's inequality 14
211 Quasinorm 14
212 Principal angles 14
213 Closed linear span 14
214 Normal basis 13
215 Trace identity 13
216 K-frame 13
217 Integer points in convex polyhedra 13
218 Absolutely convex set 12
219 Purification of quantum state 12
220 Theorems and definitions in linear algebra 12
221 Frame (linear algebra) 12
222 Spread of a matrix 11
223 Field of values 11
224 Nonnegative rank (linear algebra) 11
225 Projectivization 11
226 Fredholm's theorem 10
227 Computing the permanent 10
228 Semilinear transformation 10
229 Segre classification 9
230 Trace diagram 8
231 Quaternionic vector space 8
232 Rank factorization 8
233 Vector spaces without fields 7
234 Eigengap 7
235 Reality structure 6
236 Dual basis in a field extension less than 5 views
237 Vector quadruple product less than 5 views
238 Skew-Hamiltonian matrix less than 5 views
239 Linear algebra topics less than 5 views
240 Mixed linear complementarity problem less than 5 views
241 Whitehead's lemma less than 5 views
242 Finite dimensional von Neumann algebra less than 5 views
243 Vector spaces in mathematics less than 5 views
244 Coates graph less than 5 views
245 Stokes operator less than 5 views
246 Tapering (mathematics) less than 5 views
247 Schur–Horn theorem less than 5 views

# Encyclopedia

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by linear ones.

The main article for this category is Linear algebra.

## Related categories

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## Subcategories

This category has the following 5 subcategories, out of 10 total.

## Pages in category "Linear algebra"

The following 195 pages are in this category, out of 246 total. This list may not reflect recent changes (learn more).

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# Wiktionary

Up to date as of January 15, 2010

### Definition from Wiktionary, a free dictionary

Wikipedia has a category on:

Wikipedia

The following is a list of words related to linear algebra.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

## Entries in category “Linear algebra”

The following 42 pages are in this category, out of 42 total.