Amiinmocr

Where X;Y 2Rm n Notation Here, Rm nis the space of real m nmatrices Tr(Z) is the trace of a real square matrix Z, ie, Tr(Z) = P i Z ii Note The matrix inner product is the same as our original inner product between two vectors of length mnobtained by stacking the columns of the two matrices A less classical example in R2 is theNote this means that if a ≠ b then f(a) ≠ f(b) Definition f is onto or surjective if every y in B has a preimage Note this means that for every y in B there must be an x in A such that f(x) = y Definition f is bijective if it is surjective and injective (onetoone and onto) _____ ExamplesS y = f s ; Magnetic Fields And Forces Facts About Magnetism N 'Z"¯ ƒƒ"ƒY "¯F ƒƒbƒVƒ…