Matriissi

Matriissi is a Finnish term that translates to "matrix" in English. In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are fundamental objects in linear algebra and have applications in various fields including physics, engineering, computer science, and economics.

A matrix is typically denoted by capital letters. The dimensions of a matrix are given by the number of rows and the number of columns. For example, a matrix with m rows and n columns is called an m x n matrix. The individual elements within the matrix are usually represented by lowercase letters with subscripts indicating their row and column position, such as a_ij, where i is the row index and j is the column index.

Operations that can be performed on matrices include addition, subtraction, and multiplication. Matrix addition and subtraction are element-wise operations and require matrices of the same dimensions. Matrix multiplication, however, is a more complex operation where the product of two matrices is obtained by summing the products of corresponding entries from the rows of the first matrix and the columns of the second matrix. This operation has specific dimension requirements.

Matrices are used to represent linear transformations, systems of linear equations, and data sets. Their properties and manipulation are extensively studied in linear algebra, leading to concepts like determinants, inverses, eigenvalues, and eigenvectors, all of which have significant theoretical and practical implications. The term "matriissi" in Finnish encompasses all these mathematical concepts and their uses.