linear dependence
"Linear dependence" is a key concept in linear algebra, crucial for understanding vector spaces and systems of equations.
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Definition
C1Linear Algebra
(technical, academic)A condition where at least one vector in a set can be expressed as a linear combination of the others.
Example
- The vectors in this set exhibit linear dependence, as one can be written as a combination of the others.
C1Mathematics
(technical, academic)A property where a non-trivial combination of vectors equals the zero vector, with coefficients not all being zero.
Example
- Linear dependence in this set means there is a combination of these vectors that sums to zero.
Similar
Terms that have similar or relatively close meanings to "linear dependence":