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How are matrices used in computer graphics to rotate images?

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vector parallelogram for addition and subtraction — linear algebra One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.

In computer graphics, matrices are essential tools for manipulating geometric figures through linear transformations. To rotate an image, a program applies a specific transformation rule to the coordinates of the points that define the object.1

This process relies on matrix multiplication, which allows for efficient and compact calculations. By representing points as vectors or using homogeneous coordinates, a computer can multiply these coordinates by a rotation matrix to produce new positions for every point in the figure.231

These transformations are part of a broader application of analytic geometry, where matrices facilitate the movement, scaling, and projection of three-dimensional virtual objects onto a two-dimensional screen. Because these operations are expressed as linear combinations, they allow graphics software to perform complex visual changes—such as rotation, reflection, or stretching—with high speed and precision.321