矩阵的condition number是啥？

就是秩吗？
cond Condition number with respect to inversion Syntaxc = cond(X)
c = cond(X,p)
DescriptionThe condition number of a matrix measures the sensitivity of the solution of a system of linear equations to errors in the data. It gives an indication of the accuracy of the results from matrix inversion and the linear equation solution. Values of cond(X) and cond(X,p) near 1 indicate a well-conditioned matrix. c = cond(X) returns the 2-norm condition number, the ratio of the largest singular value of X to the smallest. c = cond(X,p) returns the matrix condition number in p-norm: norm(X,p) * norm(inv(X),p
另外这里说的1-norm 2-norm 是什么意思？

是条件数

不是。condition number一般在矩阵里被定义做最大singular value和最小singular value的比值。一般说来，如果一个矩阵的condition number大于1000，数值计算inv(A)或者解线性方程AX=Y可能会遇到严重的舍入问题，这样的问题通常被称为ill-conditioned。
最简单的解决方法是把A的diagonal entries都加上一个微小量delta以后再计算——这样做虽然会引入误差，但是可以改善ill-condition。