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Core Concept Map Language

Corollaries from Linear independence

All corollaries from Linear independence.

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[COROLLARY]

Adjoining a vector outside the span

If $S$ is linearly independent and $v\notin\operatorname{span}(S)$ , then $S\cup\{v\}$ is linearly independent.

[1]:Adding a vector to a span
[2]:Linear independence
[3]:Extend an independent set to a basis
[4]:Proof

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It leads to Basis and dimension, Seen Questions, Coordinates and bases, Diagonalisation (Eigenvalues), Seen Questions (Eigenvalues) and 1 more.

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Adjoining a vector outside the span