Column Space. Criteria for membership in the column space. The columns of A span the column space, but they may not form a basis if the column vectors are not linearly independent.
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All vectors perpendicular to the column space lie in the left null space.
Criteria for membership in the column space.
Row space | Column Space | Null space | Rank | Nullity
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In linear algebra, the column space of a matrix (sometimes called the range of a matrix) is the set of all possible linear combinations of its column. Clearly, elementary row operations do affect the column space. This is the sixth post in an article series about MIT's Linear Algebra course.
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