The identity matrix has ones on its main diagonal and zeros elsewhere, and satisfies IA=AI=A whenever the products are defined.
Ancestors (8)
Incoming links (149)
- Adjoint in weighted coordinates
- Block matrix inverse
- Cartesian basis under rotation
- Cayley-Hamilton theorem
- Choosing a different block pivot
- Closed walk
- Communicating class
- Convex optimization
- Cubically invariant second-rank tensor
- Derivative of a local inverse map
- Determinant
- Determinantal function
- Eigenvalue
- Elementary matrix
- Elementary-matrix factorization theorem
- Exponentiation by squaring
- Farkas' lemma
- Fixed-step gradient descent on a positive-definite quadratic
- Fundamental matrix of a finite absorbing Markov chain
- Givens rotation
- Haldane model
- Hermitian two-by-two matrix in the Pauli basis
- Householder reflection sending a vector to a coordinate axis
- Hydrostatic stress
- Inertia tensor
- Interior of the copositive cone
- Inverse-matrix verification test
- Irreducible Markov chain
- Iteration matrix
- Kronecker sum
- Lagrange cardinal polynomial
- Matrix inverse
- Matrix polynomial
- Matrix ring
- Matrix similarity invariants
- Matrix trace
- Moore-Penrose inverse
- Newtonian fluid stress tensor
- Orthogonal skew-symmetric matrix
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- Permanent (mathematics)
- Point-mass tidal stretching and squeezing
- Positive-definite bilinear form
- QR decomposition
- Rank-one matrix update
- Rashba effect
- Resolution of the identity in an orthonormal basis
- Ring
- Rotation matrix
- Row rank
- Shape operator
- Sherman–Morrison formula
- Similarity and the coordinate metric
- Solvability of an affine rank-one vector equation
- Sparse elimination of a four-leaf star
- Stable construction of a Givens rotation
- Symmetric bilinear form
- Trace and local volume change
- Triangular solves for LU decomposition
- Unitriangular group
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An identity matrix is a special type of square matrix that plays a key role in linear algebra. It is defined as a matrix in which all the elements of the principal diagonal are equal to 1, and all other elements are equal to 0. In mathematical notation, an identity matrix of size \( n \times n \) is denoted as \( I_n \).