Interpreting sparsity. Suppose the n-vector x is sparse, i.e., has only a few no

Question

Interpreting sparsity. Suppose the n-vector x is sparse, i.e., has only a few nonzero entries. Give a short sentence or two explaining what this means in each of the following contexts. (a) x represents the daily cash flow of some business over n days. (b) x represents the annual dollar value purchases by a customer of n products or services. (c) x represents a portfolio, say, the dollar value holdings of n stocks. (d) x represents a bill of materials for a project, i.e., the amounts of n materials needed. (e) x represents a monochrome image, i.e., the brightness values of n pixels. (f) x is the daily rainfall in a location over one year.

Explanation / Answer

Given: x is a sparse vector.i.e., It has elements all 0 except a new.

(a) In n days, business is very dull. Only a few days, we had cah flow. In all other days, there was no cash flow at al.

(b) Out of the n products or services purchased by a customer, annual dollar value was almost 0 for all products or services, except a few.

(c) Out of n stocks, only a few had portfolio, say, the dollar value holding. They were mostly 0.

(d) There was practically very small amount of n materials needed.

(e) The monochrome image, i.e., the brightness values of n pixels was almost 0, except a few.

(d) There was very much shrtage of rain fall in a location over one year.i.e., it rained only a few days in a year. Rest of the days were dry.

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