This is a basic question, but I can't find the definition on wikipedia, google, or math.stackexchange, because I only find examples of it being used in problems.

Therefore, I want to clarify: Does a non-zero vector have at least one non-zero entry or must all the entries be non-zero?

Example from wikipedia: "M is said to be positive definite if z'Mz is positive for any non-zero column vector z of n real numbers"


1 Answer 1


A non-zero vector is one with at least one non-zero entry, at least in $\mathbb{R}^n$ or $\mathbb{C}^n$.

In general, a non-zero vector is one that is not the identity element for addition of the vector space in question.


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