A rectangular array or a table-like structure that consists of numbers and elements can be defined as Matrices. A matrix is a singular form of matrices. These elements are arranged in different rows and columns. Rows can be regarded as the horizontal distribution of the numbers and columns can be defined as the vertical distribution of elements. The rows and columns can be of any number. In the matrix, various arithmetic and different operations are performed. For example, addition, multiplication, transposition, and scalar multiplication. There are various rules to be followed while performing the operations. Such as, the addition can be performed only when the number of columns and rows are the same. Similarly, multiplication can be performed only when the elements or numbers in the first rows and second columns are the same. In this article, we shall cover various topics regarding the matrices such as types of matrix, operation of matrix and do a detailed discussion about these topics.
Inverse of Matrix
As mentioned above, a rectangular array or a table-like structure that consists of numbers and elements can be defined as a Matrix. The inverse of a matrix can be defined as the other matrix which produces a different value of a matrix that gives a different multiplicative identity. There are various terms related to the inverse of a matrix. Some of them are minor, cofactor, determinant, singular matrix, adjoint of the matrix, and so on. Each element or number present in the columns and rows of the matrix can be defined as the minor. A single value representation of a matrix which is also considered as a unique value can be defined as the determinant of a matrix. When the value of the determinant is equivalent to zero, it is termed a singular matrix. Similarly, when the value is not equal to zero, it is defined as a non-singular matrix.
Various Types of Matrix
Based on the sizes of the rows, columns, and elements, the matrix has been classified into various types. Some of them are row matrix, column matrix, rectangular matrix, zero matrix, square matrix, and so on. The following points mentioned below analyze the types of a matrix in a detailed manner.
- Any matrix which consists of one row and any number of the columns can be defined as the row matrix. Rows can be defined as the horizontal distribution of numbers. Similarly, a matrix that consists of one column and any number of rows can be defined as the column matrix. Columns can be defined as the vertical distribution of elements.
- A matrix with non-equal numbers of both rows and columns can be termed as the rectangular matrix. Similarly, a matrix with equal numbers of both rows and columns can be termed as the square matrix.
- When the elements or the numbers of a matrix are constant for a given number of sizes and dimensions, then the matrix is termed as a constant matrix or constant matrices. This is the most common matrix used in mathematics along with rectangular and square matrices.
- When the value of the determinant is equivalent to zero, the matrix is known as the singular matrix. Similarly, when the value of the determinant is not equivalent to zero, the matrix is known as the non-singular matrix.
- A type of square matrix where the elements are 0 except for the elements which are attached diagonally in the matrix can be defined as the diagonal matrix.
- When the elements or numbers of the matrix are equivalent to 0 or 1, then the matrix is defined as the boolean matrix.
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