Matrix norm
matrixnorm.Rd
Computes the norm of a matrix.
Details
The function norm2
computes the norm of a matrix. Three choices
are possible:
p=1

The maximum absolute column sum norm which is defined as the maximum of the sum of the absolute valued elements of columns of the matrix.
p=2

The spectral norm is "the norm" of a matrix
X
. This value is computed as the square root of the maximum eigenvalue ofCX
, whereC
is the conjugate transpose. p=Inf

The maximum absolute row sum norm is defined as the maximum of the sum of the absolute valued elements of rows of the matrix.
Note
Since base::norm()
has become available in the R base
environment, the function fBasics::norm()
has become obsolete.
To avoid conflicts with norm()
we have renamed the fBasics' one
to norm2
.
References
Golub, van Loan, (1996); Matrix Computations, 3rd edition. Johns Hopkins University Press.
Examples
## Create Pascal Matrix:
P < pascal(5)
P
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 1 1 1 1
#> [2,] 1 2 3 4 5
#> [3,] 1 3 6 10 15
#> [4,] 1 4 10 20 35
#> [5,] 1 5 15 35 70
## Return the Norm of the Matrix:
norm2(P)
#> [1] 92.29043