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# TRANSFORMATION MATRICES

Homogeneous transformation matrices are used to represent the transformation between coordinate frames in a robotic system. These matrices can represent both translation and rotation in a unified manner.

Understanding the fundamentals of Linear Transformations is indeed essential to understand the cocepts of Transformation Matrices, their meaning and the basis of these transformations.

**LINEAR TRANSFORMATIONS**

In very basic context, Linear Transformation is a function, who takes up a vector as an input and gives out an vector as output.

Visualy speaking, a Transformation can be said to be **Linear**, if the following conditions are satisfied :
- All lines must remain line, i.e they should not get curved.
- The Origin must be fixedin the plane, and most importantly:
- Grid lines must remain Parallel and evenly spaced

### SOME IMP TERMS

1. **Basis Vectors** : These are the fundamental vectors that form the building blocks of a vector space and can be linearly combined to represent any vector in that space.In 3D space, we have i , j and k as our basis vectors along the X, Y and Z axes respectively.
2. **SCALING OF VECTORS** : This is the process of stretching, squashing or sometimes reversing the direction of any given vector.
3. **SCALAR** : These are the numbers with the relevsnce of whom the scaling occurs.
4. **SPAN OF A VECTOR** : Span is the extent of any vector wrt its spacing in the X,Y and Z axes respectively.