Matrices Formulas

Posted In: Mathematics

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

  1. An $m\ x\ n$ matrix A is a rectangular array of elements (numbers of functions) with m rows and n columns
    $A=[a_{ij}]=[\table a_11,a_12,…,a_{1n};a_21,a_22,…,a_{2n};…,…,…,…;a_{m1},a_{m2},…,a_{mn}]$
  2. Square matrix is a matrix of order $nxn$
  3. A square matrix $[a_{ij}]$ is symmetric if $a_{ij}=a_{ji},$ i.e. it is symmetric around the leading diagonal. A $4×4$ symmetric matrix:
    $[\table 2,3,1,4;3,4,2,1;1,2,5,2;4,1,2,6]$
  4. A square matrix $[a_{ij}]$ is skew-symmetric if $a_{ij}=-a_{ji}$.
    $[\table 0,3,-1,4;-3,0,-2,1;1,2,0,-2;-4,-1,2,0]$
  5. Diagonal matrix is a square matrix with all elements zero except those on the leading diagonal. A $4×4$ diagonal matrix:
    $[\table 2,0,0,0;0,3,0,0;0,0,1,0;0,0,0,5]$
  6. Unit matrix is a diagonal matrix with all diagonal elements are 1. The unit matrix is denoted by I. A $4×4$ unit matrix:
    $I_4=[\table 1,0,0,0;0,1,0,0;0,0,1,0;0,0,0,1]$
  7. A null matrix is one whose elements are all zero. A $4×4$ null matrix:
    $[\table 0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0]$

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