maatriksid

Maatriksid (Estonian for matrices) are rectangular arrays of numbers, variables, or functions arranged in rows and columns. In mathematics they represent linear transformations and systems of linear equations. The term maatriks refers to a single matrix, while maatriksid is the plural.

They are denoted by uppercase letters such as A, B, or M. An m-by-n matrix A has m rows and n columns, with entries a_ij in the i-th row and j-th column. The transpose A^T is formed by swapping rows and columns.

Matrix addition and subtraction are elementwise; scalar multiplication multiplies every entry. Matrix multiplication AB is defined when the number of columns of A equals the number of rows of B and results in an m-by-p matrix. The determinant det(A) is defined for square matrices and indicates invertibility; A is invertible if det(A) ≠ 0. The inverse A^{-1} satisfies AA^{-1}=A^{-1}A=I.

Examples include diagonal matrices, where off-diagonal entries are zero; triangular matrices (upper or lower); symmetric matrices with A^T=A; skew-symmetric with A^T=−A; orthogonal matrices with A^T A = I; the identity matrix I_n and zero matrix 0.

Matrices are used to solve linear systems, perform coordinate transformations, and in many fields such as computer graphics, statistics, and machine learning. In Estonian mathematics education, maatriksid are introduced with these same concepts and notation.