Understanding Orthogonality: Definition, Examples, and Applications

Orthogonal means that two things are at right angles to each other, or perpendicular. In other words, they are not in the same direction, but instead are at a 90-degree angle to each other.

For example, if you draw a line on a piece of paper, and then draw another line that is perpendicular to the first line, those two lines are orthogonal to each other. They are not in the same direction, but instead are at a right angle to each other.

In mathematics, orthogonality is an important concept that is used to describe the relationship between vectors and matrices. Vectors and matrices can be orthogonal to each other if they have a dot product of zero. This means that the two vectors or matrices are perpendicular to each other, and do not have any component in the same direction.

Orthogonality is also an important concept in many other fields, such as physics, engineering, and computer science. In these fields, orthogonality is often used to describe the relationship between different variables or directions, and is a key concept for understanding many phenomena and solving problems.