# Applied linear algebra strang pdf

Here, the concepts of rank and nullity do not necessarily apply. This follows applied linear algebra strang pdf the distributivity of matrix multiplication over addition.

We also touch on the row space and its relation to the kernel. A are orthogonal to each of the row vectors of A. 3, we have an illustration of the rank-nullity theorem. In fact, the computation may be stopped as soon as the upper matrix is in column echelon form: the remainder of the computation consists in changing the basis of the vector space generated by the columns whose upper part is zero. The problem of computing the kernel on a computer depends on the nature of the coefficients. Even for a well conditioned full rank matrix, Gaussian elimination does not behave correctly: it introduces rounding errors that are too large for getting a significant result. As the computation of the kernel of a matrix is a special instance of solving a homogeneous system of linear equations, the kernel may be computed by any of the various algorithms designed to solve homogeneous systems.