Orthogonality: meaning, definitions and examples

Used primarily in mathematical and scientific contexts to describe vectors or functions that are at right angles to each other.

• The orthogonality of these two vectors can be proven using the dot product.
• In signal processing, orthogonality of waveforms ensures minimal interference.

Commonly used in geometry and engineering to describe the relationship between lines, surfaces, or structures that intersect at right angles.

• The architect ensured the perpendicularity of the building's walls.
• Check the perpendicularity of the beams during assembly.

Used in everyday language and basic geometry to describe the specific 90-degree angle formed by two intersecting lines or surfaces.

• Hang the picture so that it forms right angles with the wall.
• The two streets meet at right angles.

Used mainly in mathematical, statistical, and engineering contexts to describe variables or vectors that are perpendicular to each other and have no direct influence on one another.

• The orthogonality of the vectors ensures that there is no overlap in their directions.
• In signal processing, orthogonality plays a crucial role in efficiently transmitting data.

Commonly used in statistics and probability theory to describe events that do not affect each other. It is also used more broadly in everyday language to refer to people or entities that operate autonomously.

• The independence of two random events means that the occurrence of one does not affect the probability of the other.
• Her financial independence allows her to make her own decisions without relying on others.

Used in general contexts to describe things that have no connection or relationship to one another, often implying a lack of relevance or alignment between them.

• The unrelatedness of their backgrounds made it difficult for them to find common ground.
• In the discussion, several unrelated topics were brought up, confusing the main issue.

This term is used mainly in mathematics and engineering to describe the relationship between vectors that are perpendicular to each other. It can also refer to a lack of correlation or dependence in various contexts.

• The orthogonality of the two vectors was crucial for solving the geometric problem.
• Ensuring the orthogonality of the features can improve the performance of the machine learning model.

This phrase is commonly used in probability and logic to describe two events that cannot happen at the same time.

• The concepts are in mutual exclusivity, meaning they cannot both be true simultaneously.
• In a coin toss, getting a head and getting a tail are mutually exclusive events.

Often used in statistics and probability theory, 'independence' describes two events that do not influence one another. It is also widely used in everyday language to denote self-sufficiency.

• In probability theory, two events are said to have independence if the occurrence of one does not affect the occurrence of the other.
• She values her independence and enjoys traveling alone.