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Exercise 8

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The trace of a square matrix is the sum of the entries on the main diagonal (the 1,11,1 entry plus the 2,22,2 entry, etc.; we will see the significance of the trace in Chapter Five). Show that trace(H+G)=trace(H)+trace(G)\text{trace}(H+G)=\text{trace}(H)+\text{trace}(G). Is there a similar result for scalar multiplication?

Hefferon, Linear Algebra, Maps Between Spaces, Sums and Scalar Products, Exercise 8

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.