Re: Tell whether a matrix is full rank using a calculator

In article <5ieoaoF3ouatnU1@xxxxxxxxxxxxxxxxxx>, <jcsantos@xxxxxxxx>
writes:
On 14-08-2007 21:31, isabellesup@xxxxxxxxxxx wrote:

I would like to be able to tell if a (say 5*5) matrix is full rank
by
using my graphic calculator.
My calculator does not have a built in function that computes the
rank. Is there another way to know whether a matrix is full rank?
Say
by looking at the eigenvalues (my calculator will compute the
eigenvalues), or some other method....
A square matrix is full rank if and only if its determinant is
non-null.
So, if your calculator computes determinants, just compute the
determinant of your matrix and see whether or not it is equal to 0.

Thanks all for the help.

Now what if the matrix is not square? Eigenvalues and Determinants do
not exist.

If it has more columns than lines, consider all square matrices obtained
from your original matrix be deleting some columns. If all these square
matrices have non-null determinant, than your matrix is full rank.
Otherwise, it isn't. There's a similar method if it has more lines than
columns.

If the calculator can do exact determinants, then for any non square
matrix, multiply it by its transpose in which ever order produces the
smaller square matrix, and take the determinant of that result. If that
determinant is non-zero, then the original matrix is of full rank.

If the calculator can only give approximations, one will have the
problem of determining how large in absolute value the determinant
should be to represent a truly non-zero value.

An approximate determinant smaller in absolute value than the product of
the smallest members of each row (or of each column) of the square
matrix might indicate a determinant whose exact value might be zero.
.

Relevant Pages

  • Re: Tell whether a matrix is full rank using a calculator
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  • Re: Tell whether a matrix is full rank using a calculator
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  • Re: Tell whether a matrix is full rank using a calculator
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  • Re: Tell whether a matrix is full rank using a calculator
    ... Is there another way to know whether a matrix is full rank? ... by looking at the eigenvalues (my calculator will compute the ... So, if your calculator computes determinants, just compute the ... Now what if the matrix is not square? ...
    (sci.math)
  • Re: Tell whether a matrix is full rank using a calculator
    ... Is there another way to know whether a matrix is full rank? ... by looking at the eigenvalues (my calculator will compute the ... eigenvalues), or some other method.... ... A square matrix is full rank if and only if its determinant is non-null. ...
    (sci.math)
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