y <- c(6, 9, 14)
x <- c(1, 0, 2)

print(x+y)
print(c(x,y,x+y))

# printed as column vectors
print(cbind(x,y,x+y))

z <- 2*y
print(z)

ip <- x %*% y
print(c("The inner product is ",ip))

# Two ways to compute a sum
sumy1 <- rep(1,3) %*% y
sumy2 <- sum(y)

# Some matrix calculations
newx <- rbind(c(1,0,-1),c(2,3,1))
newy <- rbind(c(4,1,1),c(0,3,2))

newx + newy

newx %*% t(newy) 

# Kronecker product
kronx <- newx %x% t(c(5,7))
kronx


i2 <- diag(2)
j2 <- matrix(rep(1,4),nrow=2,ncol=2)

# matrix inverse
newx2 <- matrix(c(6,2,3,4),nrow=2,ncol=2,byrow=T)
inewx2 <- solve(newx2)
rownames(inewx2) <- c("a","b")
colnames(inewx2) <- c("a","b")
inewx2

print("Some matrix functions")

z7 <-  newx[1,2]
z8 <-  newx[1,]
z9 <-  cbind(newx,newy)
z10 <- rbind(newx,newy)
z11 <- max(newx)
z12 <- min(newx)
z13 <- sum(newx)
z14 <- sum(newx^2)

print(c(z7,z8))
print(z9) ; print(z10)
print(c(z11,z12,z13,z14))