## Abstract

Several books[2,6] explained the normal vector transformation matrix is*$(M^{-1})^{T}$*. I always forget this formula. This time I understand it a bit in three different ways, so I will write them down here.

## Introduction

Assume matrix*M*is applied to a vector where the

*M*is a coordinate transformation matrix. For example,

*M*could be a translation, rotation, scaling, and so forth. To transform a position vector, we can just multiply this matrix

*M*. However, we may fail when we transform a normal vector by just multiplying the matrix

*M*. Several books mentioned normal transformation matrix should be $

*(M^{-1})^{T}$*[2,6].

In this article, I would like to mention about the following three issues:

- What is the problem? What is the transformation matrix of normal?
- Why may multiplying matrix
*M*fail? - Why is it an inverse of transpose of matrix
*M*?

(The references will be shown up at the end of this series.)

Next time, I would like to talk about the problem.

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