Isometry Checker - Determine if a Matrix Preserves Distances
Easily check if a transformation matrix is an isometry online. Input your matrix and find out if it preserves distances with this free Isometry Checker tool.
Enter Transformation Matrix
Input the square matrix to check if it represents an isometry. You can adjust the matrix dimensions using the buttons below.
Result
Visualization of Transformation
Visual representation of the transformation applied by the matrix. An isometry preserves lengths, so the transformed basis vectors (blue and green lines) maintain their original lengths relative to the axes.
Basis vectors transformed by the matrix.
What is an Isometry?
In mathematics, particularly in linear algebra and geometry, an isometry is a transformation that preserves distances between points. In the context of matrices, a transformation matrix is an isometry if applying it to vectors does not change their lengths. For a matrix \(M\) to be an isometry, it must satisfy the condition \(M^T M = I\), where \(M^T\) is the transpose of \(M\) and \(I\) is the identity matrix.
This tool helps you check if a given square matrix is an isometry. Simply input the matrix, and the tool will determine if it meets the criteria for preserving distances. Understanding isometries is crucial in various fields, including computer graphics, physics, and engineering, where transformations that maintain shape and size are essential.
Use this Isometry Checker to quickly verify matrices and deepen your understanding of linear transformations and their properties.