Linear Independence
<span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">In the theory of </span><a href="https://en.m.wikipedia.org/wiki/Vector_space" title="Vector space" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">vector spaces</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">, a </span><a href="https://en.m.wikipedia.org/wiki/Set(mathematics)" title="Set (mathematics)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">set</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> of </span><a href="https://en.m.wikipedia.org/wiki/Vector(mathematics)" title="Vector (mathematics)" class="mw-redirect" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">vectors</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">is said to be </span><span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 700; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">linearly dependent</span><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> if at least one of the vectors in the set can be defined as a </span><a href="https://en.m.wikipedia.org/wiki/Linear_combination" title="Linear combination" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">linear combination</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> of the others; if no vector in the set can be written in this way, then the vectors are said to be </span><span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 700; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">linearly independent</span><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">. These concepts are central to the definition of </span><a href="https://en.m.wikipedia.org/wiki/Dimension_(vector_space)" title="Dimension (vector space)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">dimension</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">.</span>