How many matrices are there

For example,. Blocks of zeros are often left blank in nondiagonal matrices also. Square matrices. Any matrix which has as many columns as rows is called a square matrix. The 2 x 2 matrix in Example 2 and the 3 x 3 matrix in Example 3 are square. If a square matrix has n rows and n columns, that is, if its size is n x n , then the matrix is said to be of order n. Triangular matrices. If all the entries below the diagonal of a square matrix are zero, then the matrix is said to be upper triangular.

The following matrix, U , is an example of an upper triangular matrix of order If all the entries above the diagonal of a square matrix are zero, then the matrix is said to be lower triangular.

The following matrix, L , is an example of a lower triangular matrix of order A matrix is called triangular if it is either upper triangular or lower triangular. A diagonal matrix is one that is both upper and lower triangular.

In the above matrix, the element in the first column of the first row is 21; the element in the second column of the first row is 62; and so on. Matrix elements. Consider the matrix below, in which matrix elements are represented entirely by symbols. There are several ways to represent a matrix symbolically. The simplest is to use a boldface letter, such as A , B , or C. Thus, A might represent a 2 x 4 matrix, as illustrated below. Please help. Ritu Ritu 1, 3 3 gold badges 19 19 silver badges 38 38 bronze badges.

Add a comment. Active Oldest Votes. Learnmore Learnmore Geoff Robinson Geoff Robinson Sign up or log in Sign up using Google. Sign up using Facebook. Matrices can be used to compactly write and work with multiple linear equations, that is, a system of linear equations.

Key Terms element : An individual item in a matrix row vector : A matrix with a single row column vector : A matrix with a single column square matrix : A matrix which has the same number of rows and columns matrix : A rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Learning Objectives Practice adding and subtracting matrices, as well as multiplying matrices by scalar numbers.

Key Takeaways Key Points When performing addition, add each element in the first matrix to the corresponding element in the second matrix. When performing subtraction, subtract each element in the second matrix from the corresponding element in the first matrix. Addition and subtraction require that the matrices be the same dimensions.

The resultant matrix is also of the same dimension. Scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction. Key Terms scalar : A quantity that has magnitude but not direction. Learning Objectives Practice multiplying matrices and identify matrices that can be multiplied together.

The product of a square matrix multiplied by a column matrix arises naturally in linear algebra for solving linear equations and representing linear transformations. Key Terms matrix : A rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory.

Learning Objectives Discuss the properties of the identity matrix. Non-square matrices do not have an identity. Proving that the identity matrix functions as desired requires the use of matrix multiplication. Licenses and Attributions. CC licensed content, Shared previously.