In this learning object, we're going to look at vectors which are "linearly
dependent" or "linearly independent". The word "dependent" means
that some vectors can be expressed in terms of others - they depend on the
others. The word "linear" describes the form of that dependence
- as a linear combination. On the following pages, we'll look at
- The formal definition of linear dependence and linear independence,
- Some examples of linearly independent and linearly dependent vectors,
- An equivalent, more practical definition of linear independence.
Prerequisites:
A basic knowledge of vectors and vector calculations and an understanding of
what the span of a set of vectors is. (See the learning object Linear
Spans for more information.) Also, a little about linear systems and their solutions (for examples) and what trivial and non-trivial solutions are.
Keywords: linearly independent vectors, linearly
dependent vectors, linear dependence relation among vectors, trivial and non-trivial solutions
 Linear
Independence |
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| Introduction | The basic definition of linear independence | Examples of linearly independent geometric vectors | A more practical form of linear independence |
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