**Contents**show

## What is the purpose of linear transformation?

Linear transformations are useful because **they preserve the structure of a vector space**. So, many qualitative assessments of a vector space that is the domain of a linear transformation may, under certain conditions, automatically hold in the image of the linear transformation.

## How are matrices used in transformations?

We can use matrices to **translate our** figure, if we want to translate the figure x+3 and y+2 we simply add 3 to each x-coordinate and 2 to each y-coordinate. If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with.

## What is the purpose of viewing matrix?

The view matrix is used **to transform a model’s vertices from world-space to view-space**.

## Why do we need matrix?

**The numbers in a matrix can represent data**, and they can also represent mathematical equations. In many time-sensitive engineering applications, multiplying matrices can give quick but good approximations of much more complicated calculations.

## What do you understand by transformation?

A transformation is **a dramatic change in form or appearance**. An important event like getting your driver’s license, going to college, or getting married can cause a transformation in your life.

## What do you mean by transformation matrix?

A transformation matrix is a matrix that **represents a linear transformation in linear algebra**. These have specific applications to the world of computer programming and machine learning.

## How do you know if a matrix is a transformation?

To do this, we must take a look at **two unit vectors**. With each unit vector, we will imagine how they will be transformed. Then take the two transformed vector, and merged them into a matrix. That matrix will be the transformation matrix.

## What is a transform of the world space to the camera point of view?

To convert points from world to camera space, we need to **multiply points in world space by the inverse of the camera-to-world matrix**. By default the camera is located at the origin and is oriented along the world coordinate system negative z-axis.

## Why is a transformation matrix 4×4?

The 4 by 4 transformation matrix uses **homogeneous coordinates**, which allow to distinguish between points and vectors. Vectors have a direction and magnitude whereas points are positions specified by 3 coordinates with respect to the origin and three base vectors i, j and k that are stored in the first three columns.

## What is the use of matrix stack and view matrix?

The matrix stack is **used to concatinate matrices**. Typically used for heirarchical models where a transformation is expressed relative to another. One can load a matrix on the stack and transform vertices in that space and then go back to the parent space by popping the stack.