A vector v = (V₁, V2, ..., Un) € R" is said to be strongly positive if vi > 0 for all i 1,..., n. Prove that if a subspace S of Rn contains a strongly positive vector, then S admits a basis of strongly positive vectors.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A vector v = (V₁, V2, ..., Un) € R" is said to be strongly positive if v;> 0 for all
i 1,...,n. Prove that if a subspace S of R" contains a strongly positive vector,
then S admits a basis of strongly positive vectors.
-
Transcribed Image Text:A vector v = (V₁, V2, ..., Un) € R" is said to be strongly positive if v;> 0 for all i 1,...,n. Prove that if a subspace S of R" contains a strongly positive vector, then S admits a basis of strongly positive vectors. -
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