Matrix Definition. Main information
Definition.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.
Matrices 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: An×m.
Entries of the matrix A are denoted aij, where i is row number, in which is an element, j is the column number.
Example.Entries of matrix A4×4:
a11 = 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 non-zero.
Example.Zero and non-zero 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 non-zero.
Example.Zero and non-zero matrix column:
non-non-zero matrix column
Definition.Main diagonal of matrix is the collection of entries aij where i = j.
Definition.Antidiagonal of matrix with size n×m is the collection of entries aij 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) = a11 + a22 + ... + ann.
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