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Vectors, Pure and Applied by T. W. Körner

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15

More distances

15.1 Distance on images(U, U)

When dealing with matrices, it is natural to say that that the matrix

images

is close to the 2 × 2 identity matrix I. On the other hand, if we deal with 104 × 104 matrices, we may suspect that the matrix B given by bii = 1 and bij = 10–3 for ij behaves very differently from the identity matrix. It is natural to seek a notion of distance between n × n matrices which would measure closeness in some useful way.

What do we wish to mean by saying that we want to ‘measure closeness in some useful way’? Surely, we ...

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