Introduction

The identity matrix, an important concept in linear algebra, is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. In this blog post, we will explore the identity matrix, its properties, and applications.

Applications

Preserving Vector Identity

One of the fundamental uses of an identity matrix is that multiplying it with any vector doesn't change the vector's identity. It is used extensively in both theoretical and applied mathematics.

where A is any matrix, I is the identity matrix, and the result is the original matrix A.

Inverse Calculation

The identity matrix is also instrumental in finding the inverse of a matrix. If A is a square matrix, then the matrix B is the inverse of A if and only if the product of A and B (in either order) equals the identity matrix.

where I is the identity matrix, and B is the inverse of A.

References

• Identity Matrix - Wikipedia
• Identity Matrix - Wolfram MathWorld