411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a0o8
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In numerical analysis, the condition number of a function measures how much the output value of the function can change for a small change in the input argument. Wikipedia: Condition number
Condition number (Matrices) (eigen)
The study of the conditioning of a matrix gives us a number that allows us to estimate whether the expected result can be considered correct.
For some (symmetric) matrices, we can choose the quotient between the maximum eigenvalues and the minimum eigenvalues of A.
The higher the quotient, the greater the rounding problems and the risk of disrupting calculations such as the inverse of a matrix.
We will see through four examples the destructive effect of a poorly conditioned matrix.
In the first example we will have
In the second example we will have
In the third example we will have
In the fourth example we will have
We will be able to observe significant calculation errors from the second example onwards.
Four examples:
Random values
Random values
Random values
Random values