Orthonormal Bases: Definition & Example


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question 1 of 3

A basis is a collection of independent vectors which _____ a space.

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1. If the basis vectors are perpendicular to each other, we have _____.

2. To normalize the vectors in a basis, divide each vector by its _____.

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About This Quiz & Worksheet

These questions allow you to find out what you remember about basis vectors. Make sure you understand what these are and how they are used.

Quiz & Worksheet Goals

In this set of quiz/worksheet questions, you'll review your knowledge of:

  • The method used to normalize vectors in a basis
  • How a perpendicular alignment affects basis vectors
  • Defining what a basis is

Skills Practiced

  • Reading comprehension - ensure that you draw the most important information from the material, such as how any vector in a space can be written
  • Critical thinking - apply relevant concepts to examine information about what orthogonal means in terms of basis vectors in a different light
  • Problem solving - use acquired knowledge to solve basis vector practice problems
  • Defining key concepts - ensure that you can accurately define main terms, such as a basis

Additional Learning

Read or watch the lesson titled Orthonormal Bases: Definition & Examples to learn more about this area of mathematics. You will be exposed to:

  • The Gram-Schmidt process
  • Examples of orthonormal bases in use
  • Other disciplines of science and math this applies to