neliömatriisiin

A square matrix is a matrix that has the same number of rows and columns. This means that for a matrix A, the number of rows is equal to the number of columns, often denoted as n x n. Square matrices are fundamental in linear algebra and have numerous applications in various fields of mathematics, science, and engineering. The dimension of a square matrix is referred to as its order.

A key property of square matrices is that they possess a determinant, a scalar value that provides important information about the matrix. The determinant can indicate whether a matrix is invertible (has a multiplicative inverse). Square matrices also have eigenvalues and eigenvectors, which are crucial for understanding linear transformations and solving systems of differential equations. Operations such as matrix addition, subtraction, and multiplication are defined for square matrices, although matrix multiplication is not commutative in general (i.e., AB is not always equal to BA). Special types of square matrices include identity matrices (with ones on the main diagonal and zeros elsewhere), zero matrices, diagonal matrices, symmetric matrices, and skew-symmetric matrices, each with unique characteristics and applications.