## ---- echo = FALSE-------------------------------------------------------
knitr::opts_chunk$set(
warning = FALSE,
message = FALSE
)
options(digits=4)
## ------------------------------------------------------------------------
A <- matrix(c(13, -4, 2, -4, 11, -2, 2, -2, 8), 3, 3, byrow=TRUE)
A
## ------------------------------------------------------------------------
ev <- eigen(A)
# extract components
(values <- ev$values)
(vectors <- ev$vectors)
## ------------------------------------------------------------------------
crossprod(vectors)
zapsmall(crossprod(vectors))
## ------------------------------------------------------------------------
library(matlib) # use the matlib package
tr(A)
sum(values)
## ------------------------------------------------------------------------
sum(A^2)
sum(values^2)
## ------------------------------------------------------------------------
det(A)
prod(values)
## ------------------------------------------------------------------------
R(A)
sum(values != 0)
## ------------------------------------------------------------------------
AI <- solve(A)
AI
eigen(AI)$values
eigen(AI)$vectors
## ------------------------------------------------------------------------
eigen(A %*% A)
eigen(A %*% A %*% A)$values
eigen(mpower(A, 4))$values
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