cond
Condition number of matrix
Description
Examples
Compute 2-Norm Condition Number of Matrix
Compute the 2
-norm condition number of the inverse
of the 3-by-3 magic square A
.
A = inv(sym(magic(3))); condN2 = cond(A)
condN2 = (5*3^(1/2))/2
Use vpa
to approximate the result.
vpa(condN2, 20)
ans = 4.3301270189221932338186158537647
Compute Different Condition Numbers of Matrix
Compute the 1-norm condition number, the Frobenius condition number,
and the infinity condition number of the inverse of the 3-by-3 magic square
A
.
A = inv(sym(magic(3))); condN1 = cond(A, 1) condNf = cond(A, 'fro') condNi = cond(A, inf)
condN1 = 16/3 condNf = (285^(1/2)*391^(1/2))/60 condNi = 16/3
Approximate these results by using vpa
.
vpa(condN1) vpa(condNf) vpa(condNi)
ans = 5.3333333333333333333333333333333 ans = 5.5636468855119361058627454652148 ans = 5.3333333333333333333333333333333
Compute Condition Number of Hilbert Matrix
Hilbert matrices are examples of ill-conditioned matrices.
Numerically compute the condition numbers of the 3-by-3 Hilbert matrix by using
cond
and vpa
.
H = hilb(sym(3)); condN2 = vpa(cond(H)) condN1 = vpa(cond(H,1)) condNf = vpa(cond(H,'fro')) condNi = vpa(cond(H,inf))
condN2 = 524.05677758606270799646154046059 condN1 = 748.0 condNf = 526.15882107972220183000899851322 condNi = 748.0
Input Arguments
A
— Input
number | vector | matrix | array | symbolic number | symbolic variable | symbolic array | symbolic function | symbolic expression
Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.
P
— Input
2
(default) | number | character vector
One of these values 1
, 2
,
inf
, or 'fro'
.
cond(A,1)
returns the1
-norm condition number.cond(A,2)
orcond(A)
returns the2
-norm condition number.cond(A,inf)
returns the infinity norm condition number.cond(A,'fro')
returns the Frobenius norm condition number.
More About
Tips
Calling
cond
for a numeric matrix that is not a symbolic object invokes the MATLAB®cond
function.
Version History
Introduced in R2012b
See Also
equationsToMatrix
| inv
| linsolve
| norm
| rank
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