Identity matrix

Dependencies:

  1. Semiring
  2. Matrix

Let $R$ be a semiring with unity. The identity matrix of size $n$, denoted as $I_n$, is a matrix in $\mathbb{M}_{n, n}(R)$ such that \[ I_n[i, j] = \begin{cases} 1 & i = j \\ 0 & i \neq j \end{cases} \]

Dependency for:

  1. Standard multivariate normal distribution
  2. Standard normal random vector on vector space
  3. General multivariate normal distribution
  4. Chapman-Kolmogorov equation
  5. Eigenpair of power of a matrix
  6. Eigenpair of affine transformation
  7. Bound on eigenvalues of sum of matrices
  8. Square matrices form a (semi)ring
  9. Full-rank square matrix in RREF is the identity matrix
  10. Inverse of a matrix
  11. Identity matrix is identity of matrix product
  12. Elementary row operation is matrix pre-multiplication
  13. AB = I implies BA = I

Info:

Transitive dependencies:

  1. Group
  2. Ring
  3. Semiring
  4. Matrix