What is the physical interpretation of "rank" of a matrix ? Why is it called "rank" ?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The rank is the dimension of the image of the matrix. A 3x3 matrix with rank 2 sends all vectors in 3-dimensional space into a 2-dimensional subset of 3-dimensional space.
See also this answer http://math.stackexchange.com/a/39902/64062
Regarding the importance of the "rank" of a matrix, and help to understand what this is, intuitively, you'll find some wonderful answers here, to a previous post at math.se:
A wonderful website for origins of mathematical terms is found here:
Click on "[R]"...scroll down to:
"Rank (of a matrix or determinant)":