What is a non-zero vector?
Understand the Problem
The question is asking for a definition of a non-zero vector, which is a vector that has a magnitude greater than zero, meaning it is not the zero vector (0,0) or (0,0,0) in higher dimensions. This concept is fundamental in vector mathematics.
Answer
A vector with magnitude not equal to zero.
A non-zero vector is a vector with a magnitude that is not equal to zero.
Answer for screen readers
A non-zero vector is a vector with a magnitude that is not equal to zero.
More Information
In a vector space, the zero vector is the vector of which all components are zero. Any vector that is not the zero vector is called a non-zero vector.
Tips
A common mistake is confusing a non-zero vector with a non-zero component of a vector. Ensure the entire vector's magnitude is considered instead of individual components.
Sources
- A nonzero vector is a vector with magnitude not equal to zero - mathwords.com
- What's a non-zero (column) vector? - Mathematics Stack Exchange - math.stackexchange.com
- Non-zero vector - PlanetMath.org - planetmath.org
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