Types of matrices
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Following are the types of a matrix.
Zero matrix
A zero matrix, denoted as
Example
Singleton matrix
A singleton matrix is a matrix with a single element.
Example
Rectangular matrix
A rectangular matrix has different numbers of rows and columns.
Example
Square matrices
A square matrix has an equal number of rows and columns.
Example
Equal matrices
Two matrices are equal if they have the same dimensions and corresponding elements are equal.
Example
Diagonal matrix
A diagonal matrix has non-diagonal elements equal to zero.
Example
Triangular matrices (upper and lower)
A lower triangular matrix has all non-diagonal elements above the main diagonal equal to zero. In contrast, an upper triangular matrix has non-diagonal elements below the main diagonal equal to zero.
Example
Scalar matrix
A scalar matrix is a diagonal matrix where all diagonal elements are the same scalar value.
Example
Identity matrix
An identity matrix, denoted as
Example
Symmetric and skew-symmetric matrices
A symmetric matrix is equal to its transpose, while a skew-symmetric matrix is one whose transpose is the negation of itself.
Example
Invertible matrices
An invertible matrix, also called a non-singular matrix, has a unique matrix inverse that, when multiplied, yields the identity matrix.
Example
Learn about orthogonal matrix.
Conclusion
Matrices play a fundamental role in mathematics and are widely applicable across various disciplines. Each matrix type holds unique properties that find practical use in different applications, from linear transformations and computer graphics to physics and engineering.
