Matrix Condition Number and Matrix Norms - Well conditioned or Ill conditioned (Numerical Methods)

In this video we define a couple of technical terms such as the "norm of a matrix" and the condition number of a matrix. We also use the condition number to determine whether the matrix is Ill conditioned or well conditioned. ITS SIMPLE!!

Calculating the NORM of a Matrix:

STEP 1

Sum up the absolute values of each component on the corresponding rows.

STEP 2

Select the largest of the "Row sums" and use that as the 'norm' of you matrix.

Calculating the condition number of the given Matrix:

STEP 1

Find the inverse of the given matrix

STEP 2

Calculate the NORM of the INVERSE of the matrix

STEP 3

Multiply the norm of the inverse by the norm of the original matrix and this is the condition number

STEP 4

If the condition number is quite large then we have an ill conditioned matrix. If the condition number is close to 1, then our matrix is well conditioned.

check out the following link for the Crout's method:

   • Crout's Method for LU Decomposition -...  

and for Doolittle Method:

   • LU Decomposition using Gaussian Elimi...  



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