linear independence

Summary

Algorithm to check for linear independence

• recall the intuition for row reduction, expressing columns as multiples of another
• if the column is not a pivot column, then its vector can be expressed as a multiple of the other vectors

additionally tells us how each linearly dependent vector is a multiple of the other vector in the set

Concept

Linear independence

• no redundant vectors

no vector is a linear combination of the others, which would allow its coefficient to cancel out

Maximum number for linear independence

Special cases

Application

Deducing original vectors from RREF form