What's a non-zero (column) vector?
By Sarah Richards
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"
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$\begingroup$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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