identiteetmaatriks

An identiteetmaatriks, or identity matrix, is a fundamental concept in linear algebra. It is a square matrix, meaning it has the same number of rows and columns, denoted by 'n'. The defining characteristic of an identity matrix is that all its diagonal elements are equal to 1, and all other elements are 0.

An identity matrix of size n x n is commonly represented by the symbol 'I' or 'I_n'. For instance, a 2x2 identity matrix would look like:

1 0

0 1

And a 3x3 identity matrix would be:

1 0 0

0 1 0

0 0 1

The identity matrix has a crucial property: when multiplied by any compatible matrix, it leaves that matrix unchanged. This is analogous to the number 1 in scalar multiplication, where any number multiplied by 1 remains the same. In matrix algebra, if A is an m x n matrix, then A * I_n = A and I_m * A = A.

This property makes the identity matrix essential for various operations in linear algebra, including solving systems of linear equations, finding matrix inverses, and representing linear transformations. It serves as the multiplicative identity for matrices, playing a pivotal role in understanding matrix properties and manipulations.