Enhetsmatrix

Enhetsmatrix, also known as an identity matrix, is a fundamental concept in linear algebra. It is a square matrix that has ones on the main diagonal and zeros everywhere else. The main diagonal runs from the top-left corner to the bottom-right corner of the matrix.

The symbol for the identity matrix is typically the letter I, often with a subscript indicating its dimension. For example, I_n represents an n x n identity matrix. A 2x2 identity matrix, denoted as I_2, would look like this:

1 0

0 1

A 3x3 identity matrix, I_3, would be:

1 0 0

0 1 0

0 0 1

The key property of an identity matrix is that when it is multiplied by any other matrix of compatible dimensions, the result is that other matrix. This makes it analogous to the number 1 in scalar multiplication, where multiplying any number by 1 yields the original number. For a matrix A, the identity matrix I satisfies AI = IA = A.

Identity matrices are crucial in various mathematical operations, including solving systems of linear equations, matrix inversion, and transformations in geometry. They serve as the multiplicative identity in the ring of square matrices.