Weighted Norms

• \(||x||^2_W\)
• t(x) %*% (W %x% x) (W is a weight matrix)

W <- matrix(1:9, ncol = 3, nrow = 3)
W

##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

x <- c(2, -1, 1)

W %*% x

##      [,1]
## [1,]    5
## [2,]    7
## [3,]    9

z <- t(x) %*% (W %*% x)
z

##      [,1]
## [1,]   12