Linear Dependence

Linear dependence occurs when one or more vectors in a set can be expressed as a combination of others within that set. In practical terms, this means that some of the vectors don't add new directions or information; they are redundant because they can be formed by scaling and adding the others. For example, if two vectors point in the same line, one is just a scaled version of the other, making them linearly dependent. Recognizing dependence helps identify the core set of vectors that truly span a space without unnecessary duplicates.