3: The Fundamental Subspaces
( \newcommand{\kernel}{\mathrm{null}\,}\)
- 3.4: Left Null Space
- If one understands the concept of a null space, the left null space is extremely easy to understand.
- 3.5: Row Space
- The row space of the m-by-n matrix A is simply the span of its rows.
- 3.8: Supplements - Subspaces
- A subspace is a subset of a vector space that is itself a vector space. The simplest example is a line through the origin in the plane. For the line is definitely a subset and if we add any two vectors on the line we remain on the line and if we multiply any vector on the line by a scalar we remain on the line. The same could be said for a line or plane through the origin in 3 space.
- 3.9: Supplements - Row Reduced Form
- A central goal of science and engineering is to reduce the complexity of a model without sacrificing its integrity. Applied to matrices, this goal suggests that we attempt to eliminate nonzero elements and so 'uncouple' the rows.