Abstract
Consider a finite set of vectors over an arbitrary field. Of course, each subset of this set is either linearly independent or linearly dependent. Also, any subset of a linearly independent subset of the original set is itself linearly independent. Further, if I and J are two linearly independent subsets of the original subset with |I|=|J|+1, then there exists an element of I which, together with J, forms a linearly independent set of |I| vectors.
I am a little world made cunningly of elements.
Holy Sonnets, Annunciation — John Donne
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© 1992 Springer Science+Business Media New York
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Foulds, L.R. (1992). Matroids. In: Graph Theory Applications. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0933-1_10
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DOI: https://doi.org/10.1007/978-1-4612-0933-1_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97599-3
Online ISBN: 978-1-4612-0933-1
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