Category:Linear algebra
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear maps (or linear transformations), and systems of linear equations in finite dimensions. 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 a linear model.
- The main article for this category is Linear algebra.
Related categories
Wikimedia Commons has media related to: Linear algebra(previous 200) (next 200)
Subcategories
This category has the following 7 subcategories, out of 10 total.
D
M
N
S
Pages in category "Linear algebra"
The following 193 pages are in this category, out of 229 total. Updates to this list can occasionally be delayed for a few days.
A
- Absolutely convex set
- Adjugate matrix
- Affine space
- Affine transformation
- Antilinear map
- Antiunitary
- Asymmetric norm
B
- Balanced set
- Barycentric coordinates (mathematics)
- Basis (linear algebra)
- Basis function
- Bicomplex number
- Bidiagonal matrix
- Binomial inverse theorem
- Bra-ket notation
C
- Canonical basis
- Category of vector spaces
- Cauchy–Schwarz inequality
- Cayley–Hamilton theorem
- Centrosymmetric matrix
- Change of bases
- Change of basis
- Characteristic polynomial
- Choi's theorem on completely positive maps
- Codimension
- Coefficient matrix
- Cofactor (linear algebra)
- Column space
- Column vector
- Commutation matrix
- Complex conjugate vector space
- Conformable matrix
- Conjugate transpose
- Coordinate space
- Coordinate vector
- Cramer's rule
- Cross product
D
- Defective matrix
- Delta operator
- Determinant
- Dimension
- Dimension (vector space)
- Dimension theorem for vector spaces
- Direct sum of modules
- Direction vector
- Dot product
- Dual basis
- Dual basis in a field extension
- Dual number
- Dual space
- Duplication matrix
E
- Eigendecomposition of a matrix
- Eigenplane
- Eigenvalue, eigenvector and eigenspace
- Elementary matrix
- Euclidean space
- Euclidean subspace
- Examples of vector spaces
F
F cont.
- Flat (geometry)
- Frame of a vector space
- Fredholm alternative
- Fredholm's theorem
- Frobenius normal form
- Fundamental theorem of linear algebra
G
- General linear group
- Generalizations of Pauli matrices
- Generalized eigenvector
- Generalized singular value decomposition
- Gershgorin circle theorem
- Golden-Thompson inequality
- Graded vector space
- Gram–Schmidt process
H
- Hamming space
- Hilbert space
- Hilbert–Poincaré series
- Homogeneous coordinates
- Homogeneous function
- Homogeneous linear equation
- Householder transformation
- Hyperplane
I
- Identity matrix
- Immanant of a matrix
- Indeterminate system
- Invariant subspace
- Invariants of tensors
- Inverse eigenvalues theorem
- Invertible matrix
J
K
L
- Lattice reduction
- Leibniz formula for determinants
- Levi-Civita symbol
- Line segment
- Line-line intersection
- Linear combination
- Linear complementarity problem
- Linear complex structure
- Linear functional
- Linear independence
- Linear least squares
- Linear map
- Linear space
- Linear span
- Linear subspace
- List of linear algebra references
- List of vector spaces in mathematics
M
- Main diagonal
- Majorization
- Matrix (mathematics)
- Matrix addition
- Matrix calculus
- Matrix congruence
- Matrix determinant lemma
- Matrix norm
- Matrix pencil
- Matrix theory
- Modal analysis using FEM
N
N cont.
O
- Orientation (mathematics)
- Orthogonal Procrustes problem
- Orthogonal complement
- Orthogonality
- Orthogonalization
- Orthographic projection (geometry)
- Orthonormal basis
- Orthonormality
- Overdetermined system
P
- Partial trace
- Peetre's inequality
- Permanent
- Perron–Frobenius theorem
- Polynomial basis
- Principal axis theorem
- 3D projection
- Projection (linear algebra)
- Projection-valued measure
- Pseudoscalar
- Pseudovector
- Purification of quantum state
Q
R
- Rank (linear algebra)
- Rank-nullity theorem
- Rayleigh quotient
- Real matrices (2 x 2)
- Reality structure
- Reduction (mathematics)
- Reflection (linear algebra)
- Relative dimension
- Resolvent set
- Row and column spaces
- Row equivalence
- Row space
- Row vector
- Rule of Sarrus
S
- Scalar (mathematics)
- Scalar multiplication
- Schmidt decomposition
- Schur complement
- Segre classification
- Self-adjoint
- Semi-simple operator
- Sesquilinear form
- Seven-dimensional cross product
- Shear mapping
- Shear matrix
- Sherman–Morrison formula
- Similarity (geometry)
- Singular value decomposition
- Skew-Hamiltonian matrix
- Special linear group
- Spectral theorem
- Spectral theory
- Spinors in three dimensions
- Split-complex number
- Spread of a matrix
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