Transforming Space with Math

A linear transformation is a special kind of function that moves or changes vectors in a predictable way using matrices. These transformations include stretching, rotating, or flipping the space.

• Stretching: Making all vectors longer or shorter.
• Rotating: Turning vectors around the origin.
• Reflecting: Flipping vectors over a line or plane.

The Matrix Connection

Every linear transformation can be represented by a matrix. If you multiply a vector by a matrix, the result is a new vector that’s been transformed.

\[ T(\vec{v}) = A\vec{v} \]

Real-World Uses

Linear transformations are used in computer graphics, robotics, and even in solving puzzles!

Hands-On

• Rotate the point \( (1, 0) \) by 90 degrees using a rotation matrix.
• Stretch \( (2, 3) \) by a factor of 2 using a scaling matrix.