
Matrix Definition. Main informationPage Navigation:
Matrix definitionDefinition. Matrix with size n×m is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns, which consisting of n rows and m columns.The number of rows and columns are defined the matrix size. Matrix notationMatrices are commonly written in box brackets or large parentheses:
The matrix usually denoted by capital letters of the Latin alphabet. The matrix comprising n rows and m columns, called the matrix of size n×m. Also, the size of the matrix is written following way: A_{n×m}. Matrix entriesEntries of the matrix A are denoted a_{ij}, where i is row number, in which is an element, j is the column number.
Example. Entries of matrix A_{4×4}:
a_{1}_{1} = 4 Definition. Matrix row is zero if all of its elements equal to zero.Definition. If at least one of the elements of the matrix row is not zero, the row is called a nonzero.Example. Zero and nonzero matrix row:
Definition. Matrix column is zero if all of its elements equal to zero.Definition. If at least one of the elements of the matrix column is not zero, the column is called a nonzero.Example. Zero and nonzero matrix column:
nonnonzero matrix column Matrix diagonalDefinition. Main diagonal of matrix is the collection of entries a_{ij} where i = j.Definition. Antidiagonal of matrix with size n×m is the collection of entries a_{ij} where i + j = n + 1.Example. Main diagonal and antidiagonal of matrix:
Definition. The trace of square matrix A is defined to be the sum of the elements on the main diagonal.Definition. The trace of matrix is denoted as tr(A) = a_{11} + a_{22} + ... + a_{nn}. MatrixMatrix Definition. Main informationSystem of linear equations  matrix formTypes of matricesMatrix scalar multiplicationAddition and subtraction of matricesMatrix multiplicationTranspose matrixElementary matrix operationsDeterminant of a matrixMinors and cofactors of a matrixInverse matrixLinearly dependent and independent rowsRank of a matrix Add the comment 