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# Matrix arithmetic
des <- matrix(data = c(9, 5, 8, 4), nrow = 2, byrow = FALSE); des
des + des; des * 2; des * des; 1 / des; des ^ 2; des %% 3
des + 1:3 # warning with differing lengths
# Matrix multiplication
tree <- matrix(data = 1:12, nrow = 3, byrow = FALSE); tree
t(tree) %*% tree
crossprod(tree); tcrossprod(tree)
identical(t(tree) %*% tree, crossprod(tree))
# Matrix inversion
des2 <- solve(des); des2
all.equal(des2 %*% des, des %*% des2) # TRUE
library(MASS); ginv(des)
# Other matrix functions
upper.tri(x = des, diag = TRUE) # Upper triangular part: logical values
des3 <- des # Upper triangular part: values
des3[lower.tri(x = des, diag = FALSE)] <- 0; des3
det(des) # determinant
sum(diag(des)) # trace
qr(des)$rank # rank
library(Matrix); rankMatrix(des)
t(des) # transpose
eigen(des) # eigenvalue and eigenvector
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