ühikmaatriksit

Aühikmaatriksit, also known as the identity matrix, is a square matrix in linear algebra. It is characterized by having ones on the main diagonal and zeros everywhere else. The main diagonal consists of the elements from the top-left corner to the bottom-right corner of the matrix. A key property of theühikmaatriksit is that when multiplied by any other matrix of compatible dimensions, it leaves the other matrix unchanged. This is analogous to the number one in scalar multiplication, where multiplying a number by one results in the same number.

Theühikmaatriksit is typically denoted by the letter I, often with a subscript indicating its dimension, such as I_n for an n x n identity matrix. For example, the 2x2ühikmaatriksit is represented as [[1, 0], [0, 1]], and the 3x3ühikmaatriksit is represented as [[1, 0, 0], [0, 1, 0], [0, 0, 1]]. The identity matrix plays a crucial role in various matrix operations and concepts, including matrix inversion, solving systems of linear equations, and defining linear transformations. It is the multiplicative identity in the ring of square matrices.