Properties of Condition Number

Example

Go to Find Condition Number to see worked examples of finding the condition number given various matrices.

Condition Number with the Identity Matrix

For an array where is the Identity Matrix the condition number will be scaled by exactly.

Condition Number with Rotation Matrix

Whenever we have the Rotation Matrix the condition number will stay the same.

Condition Number with Diagonal Matrices

For a diagonal matrix array with entries Then we have

Proof:

Step 1: (Show )
Step 2: (Show )
where is an arbitrary unit vector of the form:
Where the 1 corresponds to the index of when multiplied with so:
and