#############
# Section 7
#############

help(Arithmetic)

help(Math) #Then click methods and scroll to Math

help(Syntax)

help(+)
help("+")

#Math functions
sqrt(3:10)
abs(-3:3)
sin(90)
sin(90*pi/180)
exp(-3:3)
log(-3:3)
factorial(8)
choose(6,2)

# Operations on vectors

myvec <- (1:4)*pi

myvec

myvec*myvec

myvec+myvec

myvec^2

2*myvec^2

(2*myvec)^2

t(myvec) * myvec

t(myvec) %*% myvec

set.seed(34) # just so you will get the same results as I do:

mymat <- matrix(rnorm(16), nc=4)

solve(mymat,myvec)

solve(mymat)

solve(mymat) %*% mymat

round(solve(mymat) %*% mymat, digits=0)

nrow(mymat)

ncol(mymat)

dim(mymat)

newmat <- rbind(myvec-1, 2*myvec)

newmat2 <- cbind(myvec-1, 2*myvec)

newmat %*% newmat2

cbind(newmat, 2*newmat)

myvec

as.matrix(myvec)

#Arithmetic operations on an entire matrix
a=matrix(1:25,ncol=5)
a
a^2

#Matrices vs. vectors
myvec=1:10
dim(myvec)
colvec=as.matrix(myvec)
attributes(colvec)
tcolvec=t(myvec)
dim(tcolvec)
tcolvec

set.seed(21) # just so you will get the same results as I do:

unif.vec <- round(runif(25, min=10, max=20),1)
a<-matrix(unif.vec,nrow=5,ncol=5)

#More matrix operations
diag(10)
b=1:5
solve(a,b)
a%*%solve(a,b)
b
solve(a)
a%*%solve(a)
round(a%*%solve(a),1)
rbind(a,b)
cbind(a,b)