Unformatted text preview: Notes on linear algebra (Monday 17th October. 2016, 23:10) page 10 they make it easier to see what entry is going where.) On the other hand. the two matrices ( I: ) and ( c d ) cannot be added (since they have different dimen- - 9
slons ). Definition 2.10 is often laconically summarized as follows: ”Matrices are added
entry by entry” (or “entrywise”). This simply means that each entry of the sum
A —|— B is the sum of the corresponding entries of A and B ;. nothing fancy is going
on. So we now know hot add two matrices. Deﬁnition 2.11. Let A be a matrix. and A be a number. Then. AA (or A - A)
denotes the matrix obtained by multiplying each entry of A by A. In other
words: If A is an a X m-matrix, then
AA : (AAirl)1gign.1gj£m'
The matrix AA is often called ”A times A”. The procedure of transforming A into AA is called scaling the matrix A by A. (Sometimes we say ”multiplying” instead of ”scaling", but “scaling" is more precise.)
We write —A for (—1) A. .1 ,./abc\ anAbAc\...
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