HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 336

The condition number of a singular matrix is infinity. The condition number of a non-singular matrix is a measure of how close the matrix is to being singular. The larger the value of the condition number, the closer it is to singularity. (A singular matrix is one for which the inverse does not exist). Try the following exercise for matrix condition number on matrix A33. The condition number is COND(A33) , row norm, and column norm for A33 are shown to the left. The corresponding numbers for the inverse matrix, INV(A33), are shown to the right: Since RNRM(A33) > CNRM(A33), then we take ||A33|| = RNRM(A33) = 21. Also, since CNRM(INV(A33)) < RNRM(INV(A33)), then we take ||INV(A33)|| = CNRM(INV(A33)) = 0.261044... Thus, the condition number is also calculated as CNRM(A33)*CNRM(INV(A33)) = COND(A33) = 6.7871485... Function RANK Function RANK determines the rank of a square matrix. Try the following examples: The rank of a matrix The rank of a square matrix is the maximum number of linearly independent rows or columns that the matrix contains. Suppose that you write a square matrix An×n as A = [c1 c2 ... cn], where ci (i = 1, 2, ..., n) are vectors representing the columns of the matrix A, then, if any of those columns, say ck, ∑ can be written as ck = dj ⋅cj, j≠k , j∈{1,2,...,n} Page 11-10