A vector space over a field F which also has an associative product defined on the vectors is called an associative F-al

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A Vector Space Over A Field F Which Also Has An Associative Product Defined On The Vectors Is Called An Associative F Al 1 (39.04 KiB) Viewed 35 times

A vector space over a field F which also has an associative product defined on the vectors is called an associative F-algebra. Another example of an associative F-algebra: the real vector space, R[x] of real polynomials in an indeterminate x. Exercise 32. For the real vector space, R[x] define linear transformations L and D via L₂(f) = xf D(f) = = dx Show that DL-LD = I, where I is the identity map. Hint: It suffices to show that the claimed identity holds for a basis of R[x].