Coefficient - Linear Algebra

Linear Algebra

In linear algebra, the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given


M = \begin{pmatrix}
1 & 2 & 0 & 6 \\
0 & 2 & 9 & 4 \\
0 & 0 & 0 & 4 \\
0 & 0 & 0 & 0
\end{pmatrix}.

The leading coefficient of the first row is 1; 2 is the leading coefficient of the second row; 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.

Though coefficients are frequently viewed as constants in elementary algebra, they can be variables more generally. For example, the coordinates of a vector in a vector space with basis, are the coefficients of the basis vectors in the expression

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