Transcription of Linear algebra in R - UH
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Linear algebra in R - UH
Linear algebra in RS ren H jsgaardFebruary 15, 2005 Contents1 Introduction12 Vectors .. Transpose of vectors .. Multiplying a vector by a number .. Sum of vectors .. (Inner) product of vectors .. The length (norm) of a vector .. The 0 vector and 1 vector .. Orthogonal (perpendicular) vectors ..53 Matrices .. Multiplying a matrix with a number .. Transpose of matrices .. Sum of matrices .. Multiplication of a matrix and a vector .. Multiplication of matrices .. Vectors as matrices .. Some special matrices .. Inverse of matrices .. Solving systems of Linear equations .. Trace .. Determinant .. Some additional rules for matrix operations .. Details on inverse matrices* .. Inverse of a 2 2 matrix* .. Inverse of diagonal matrices* .. Generalized inverse* .. Inverting ann nmatrix*.
n) to emphasize that its length n. > rep(0, 5) [1] 0 0 0 0 0 > rep(1, 5) [1] 1 1 1 1 1 2.8 Orthogonal (perpendicular) vectors Two vectors v 1 and v 2 are orthogonal if their inner product is zero, written v 1 ⊥ v 2 ⇔ v 1 ·v 2 = 0 > v1 <- c(1, 1) > v2 <- c(-1, 1) …
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