"Orthogonals" Pronounce,Meaning And Examples

"Orthogonals" Meaning

In mathematics and geometry, orthogonals refer to a relationship between two lines, planes, or curves where they intersect perpendicularly or at a right angle. In other words, if two lines or surfaces are said to be orthogonal or perpendicular to each other, it means that they form a 90-degree angle (or π/2 radians) at the point of their intersection.

"Orthogonals" Examples

Examples of "Orthogonals"

1. Mathematics

A set of orthogonal vectors is a set of vectors that are perpendicular to each other, meaning that the dot product of any two vectors is zero. In this sense, the standard basis vectors for a Euclidean space are orthogonal.

2. Graphics and Design

In computer graphics, orthogonals refer to the lines or shapes that are drawn at right angles to each other. This is often used in the creation of architectural drawings or 3D models.

3. Computing

In coding theory, orthogonals are used to create error-correcting codes. For example, the Hadamard matrix is a square matrix of 0s and 1s that is orthogonal, meaning its rows and columns are perpendicular.

4. Signal Processing

In signal processing, orthogonals are used to analyze or separate signals. For example, a filter can be designed to be orthogonal to a specific signal, allowing it to be removed or filtered out.

5. Physics

In quantum mechanics, orthogonals are used to describe the relationship between wave functions. Two wave functions are said to be orthogonal if the integral of their product is zero, meaning they do not interfere with each other.

Note: These examples are not exhaustive, and the concept of orthogonals is used in many other fields as well.