Norm | R Documentation |
The Norm
function calculates several different types of vector
norms for x
, depending on the argument p
.
Norm(x, p = 2)
x |
Numeric vector; matrices not allowed. |
p |
Numeric scalar or Inf, -Inf; default is 2 |
Norm
returns a scalar that gives some measure of the magnitude
of the elements of x
. It is called the p
-norm for values
-Inf \le p \le Inf
, defining Hilbert spaces on R^n
.
Norm(x)
is the Euclidean length of a vecor x
; same as
Norm(x, 2)
.
Norm(x, p)
for finite p is defined as sum(abs(A)^p)^(1/p)
.
Norm(x, Inf)
returns max(abs(x))
,
while Norm(x, -Inf)
returns min(abs(x))
.
Numeric scalar (or Inf
), or NA
if an element of x
is NA
.
In Matlab/Octave this is called norm
; R's norm
function
norm(x, "F")
(‘Frobenius Norm’) is the same as Norm(x)
.
norm
of a matrix
Norm(c(3, 4)) #=> 5 Pythagoras triple
Norm(c(1, 1, 1), p=2) # sqrt(3)
Norm(1:10, p = 1) # sum(1:10)
Norm(1:10, p = 0) # Inf
Norm(1:10, p = Inf) # max(1:10)
Norm(1:10, p = -Inf) # min(1:10)
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