X <- matrix(c(1,2,1,3,3,4,3,2,1,7,5,4),2,6)
colnames(X)=paste("x",1:6,sep="")
cat("\nLa matrix X y sus vectores suma y promedio son:");cbind(X,Suma=rowSums(X),Promedio=1/6*rowSums(X))

c = 1:6
sum = c(0,0)
for (i in c )
    sum = sum+c[i]*X[,i]
sum    

# código para hacer la gráfica
# Rojas D.A y Pardo C.E
# no es necesario entenderlo
x1 <- 2
y1 <- 3
x2 <- 5
y2 <- 7
dist_euclidiana <- sqrt((x2 - x1)^2 + (y2 - y1)^2)
plot(c(x1, x2), c(y1, y2), type = "n", xlab = "X", ylab = "Y",
     xlim=c(-0,5), ylim=c(0,8)#,main = "Distancia Euclidiana en R2"
     ,asp=1,las=1,main="Distancia euclidiana"
    )
abline(v=-1:6,h=0:8,col="gray80") # grilla
abline(v=0,h=0,col="darkgreen") # ejes
points(x1, y1, col = "red", pch = 16)
points(x2, y2, col = "blue", pch = 16)
segments(x1, y1, x2, y2, col = "black", lty = 2)
text(x1, y1, labels = paste("(", x1, ",", y1, ")", sep = ""), pos = 4)
text(x2, y2, labels = paste("(", x2, ",", y2, ")", sep = ""), pos = 2)
text((x1 + x2) / 2, (y1 + y2) / 2, labels = sprintf("Distancia = %.2f", dist_euclidiana), pos = 3)
segments(x1, y1, x1, y2, col = "red", lty = 3)   
segments(x1, y2, x2, y2, col = "blue", lty = 3)   
segments(x1, y1, x2, y2, col = "green", lty = 1)  
text(x1 - 0.2, (y1 + y2) / 2, labels = "Altura", pos = 4, col = "red")
text((x1 + x2) / 2, y2 + 0.2, labels = "Base", pos = 3, col = "blue")
text((x1 + x2) / 2, (y1 + y2) / 2, labels = "Hipotenusa", pos = 1, col = "green")


X

t(X)

as.numeric(t(X[,1])%*%X[,2])->x.y
cat("El producto escalar entre x,y es:",x.y)

t(X)%*%X->prodsPunto
prodsPunto

normas=sqrt(diag(prodsPunto))
round(t(normas),2)

as.dist(prodsPunto)

round(dist(t(X)),2)

rownames(X) = paste("V",1:2,sep="")
plot(t(X),las=1,xlim=c(0,5),ylim=c(0,7),asp=1)
text(t(X),colnames(X),pos=2) 
abline(v=-1:6,h=0:7,col="gray80") # grilla
abline(v=0,h=0,col="darkgreen") # ejes