Neliötaulukoilla

Neliötaulukoilla refers to matrices in Finnish. A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The elements of a matrix are typically denoted by lowercase letters with two subscripts, where the first subscript indicates the row number and the second subscript indicates the column number. For example, an element in the second row and third column of matrix A would be denoted as a₂₃.

Matrices are fundamental objects in linear algebra and have wide-ranging applications in various fields such as physics, engineering, computer science, economics, and statistics. They can be used to represent systems of linear equations, transformations in geometry, data sets, and much more.

The dimensions of a matrix are described by the number of rows and the number of columns. A matrix with m rows and n columns is said to be of size m x n. If m = n, the matrix is called a square matrix, and the elements aᵢᵢ are called diagonal elements.

Basic operations can be performed on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Matrix addition and subtraction are performed element-wise, provided the matrices have the same dimensions. Scalar multiplication involves multiplying each element of the matrix by a scalar value. Matrix multiplication is a more complex operation that requires the number of columns in the first matrix to equal the number of rows in the second matrix. The result of multiplying an m x n matrix by an n x p matrix is an m x p matrix.