# This is a file of R commands illustrating basic matrix operations.
# 
# Read in Theil's data together with row and column labels.
yx <- read.table("matrixalg.data") # Read in the data frame
# Attach database xy to the R search path so objects in xy can
# be accessed by name.
attach(yx)
# Divert output from console to file matrixalR.out
# sink("matrixalg.Rout")
yx  # print yx
y <- as.matrix(yx[,1])  # Copy first column of yx to vextor y
y
x <- as.matrix(yx[,2:3])  # Copy remaining columns of yx to matrix x
x
n <- nrow(x)  # Number of rows in maxtrix x
n
x <- cbind(1, x)  # Create nx3 design matrix by concatenation
x
y2 <- y^2  # Square the elements of y
y2
y2sum <- sum(y2)  # Sum the elements of y2
y2sum
ynorm <- sqrt(y2sum)  # Calculate the norm or length of y
ynorm
u <- as.matrix(x[,2])  # Copy the second column of x to vector u
u
unorm <- sqrt(sum(u^2))  # Calculte the norm of u in one step
unorm
z <- as.matrix(x[,1] + x[,2])  # Add the first two columns of x
z
w <- as.matrix(2*x[,1])  # Scalar multiplication of a vector
w
ip <- t(y) %*% u  # Calculte the innner or dot product of y and u
ip
cosyu <- ip/(ynorm*unorm)  # Calculate the cosine of the angle between y and u
cosyu
angleyu <- acos(cosyu)  # Angle between y and u in degrees
angleyu
rankx = qr(x)$rank  # Compute rank of x by qr decomposition
rankx
singvalx <- svd(x)$d  # Check rank by counting nonzero singular values
singvalx
xtx <- t(x) %*% x  # Multiply x' by x
xtx
detxtx <- det(xtx)  # Calculate determinant of xtx
detxtx
xtxi <- solve(xtx)  # Get inverse of xtx
xtxi 
bols <- xtxi %*% t(x) %*% y  # OLS estimate of regression coefficients
bols
resid <- y - x %*% bols  # OLS residuals
resid
xr <- t(x) %*% resid  # Check orthogonality of regressors and residuals
xr
#sink() #End diversion of output to file
q()   # Quit R