• rank(A)—Returns the rank, or the number of linearly independent columns, of A.
• geninv(A)—Returns L, the generalized (pseudo) inverse of A, which gives the least-squares solution to a system of equations. If x = L · b, then x is the minimum of |A·x − b|2. If A is square, and nonsingular, then geninv returns the transpose matrix A-1.
If A has full rank (all columns are linearly independent), then geninv returns L, the left inverse of A, that is, L · A = I. In this case, L = (AT · A)-1 · AT.
The geninv function is dependent on TOL, so for matrices that are nearly singular, adjusting this value may produce a better result.
The geninv function is based on a routine from the book Nash, J.C.,Compact Numerical Methods for Computers: Linear Algebra and Functional Minimization, John Wiley & Sons, New York, 1979.
• rref(A)—Returns the row-reduced echelon form of A.
Arguments
• A is a real vector or matrix. For geninv, the number of rows must be greater than or equal to the number of columns.