Fuzzy Set and Its Extension

7Fuzzy Matrices and Determinants

7.1 Basic Matrix Theory

In this section we give some basic notions of ordinary matrix theory that is essential to make the book self‐contained one. A matrix is a set of numbers with finite rows and columns. Since data is written in tabular form, it is very easy to consider the table as matrix. Only by removing the lines between the data, the table can become a matrix. The horizontal entries of the table become the rows of the matrix and the vertical entries of the table become the columns of the matrix. An example of four rows and five columns is shown,

From the number of rows and columns, one can find the order of a matrix. In this case, the order of matrix is 4 × 5.

We can also interchange the rows and columns of the matrix. If we interchange the second row with the fourth row, we get an interchanged matrix,

Similarly, one can interchange the columns.

If a matrix has only columns then it is called a column matrix and if a matrix has only one row, it is called row matrix. If a matrix has equal number of rows and columns, it is called a square matrix.

A matrix can be represented in a general way with m rows and n columns. Each element is represented by a_ij which means the element a is in ith row and jth column of the matrix where i = 1, 2, 3, ...