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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 85 Proposition 3.55. Let a E N. Let a and v be two distinct elements of {1,2, . . . , a}. Let A be a number. Then, the matrix Ail? has the following entries: 0 All its diagonal entries are 1. 0 Its (a, ’0)-th entry iS 2L. o All its remaining entries are 0. Proof ofPropositioa 3.55. Recall that EM, is the a x a-matrix whose (a, o)-th entry is 1 and whose all other entries are 0 (indeed, this is how Em, was defined). Since matrices are scaled entry by entry, we can therefore conclude how AEHIU looks like: Namely, AEHIU is the a X a-matrix whose (a, o)-th entry is A - 1 = A and whose all other entries are A ' O = 0. Thus, we know the following: o The matrix In is the a X n-matrix whose diagonal entries are 1,r and whose all other entries are 0. o The matrix AEaro is the n X a-matrix whose (a, o)-th entry is A, and whose all other entries are 0. Qinrn mnI-r-irfine raw} ardlrlnrq Joni-1411' 11v nnHtr 1am r911 +1111: inFnr hn‘mr I. _|_ A F‘_ lnnln: ...
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