# Definition of column space of a matrix

math.la.d.mat.col_space

# Column space of a matrix

Definition of the column space of a matrix; column space is a subspace; comparison to the null space; definition of a linear transformation between vector spaces; definition of kernel and range of a linear transformation

##### math.la.d.lintrans.range.arb
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August 25th, 2017
7 years ago
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# Column and Row Spaces - A First Course in Linear Algebra

A matrix-vector product (Definition MVP) is a linear combination of the columns of the matrix and this allows us to connect matrix multiplication with systems of equations via Theorem SLSLC. Row operations are linear combinations of the rows of a matrix, and of course, reduced row-echelon form (Definition RREF) is also intimately related to solving systems of equations. In this section we will formalize these ideas with two key definitions of sets of vectors derived from a matrix.