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If Is an Invertible (Square) Matrix with Singular Value

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If If   is an invertible (square) matrix with singular value decomposition   , then a singular value decomposition for   is given by   . is an invertible (square) matrix with singular value decomposition If   is an invertible (square) matrix with singular value decomposition   , then a singular value decomposition for   is given by   . , then a singular value decomposition for If   is an invertible (square) matrix with singular value decomposition   , then a singular value decomposition for   is given by   . is given by If   is an invertible (square) matrix with singular value decomposition   , then a singular value decomposition for   is given by   . .


Definitions:

Nondiversifiable Risk

Risk that cannot be eliminated by investing in many projects or by holding the stocks of many companies.

Diversifiable Risk

Risk that can be eliminated either by investing in many projects or by holding the stocks of many companies.

Expected Return

Expected return is the anticipated profit or loss from an investment, factoring in all possible outcomes weighted by their probabilities.

Asset Beta

A constant that measures the sensitivity of an asset’s return to market movements and, therefore, the asset’s nondiversifiable risk.

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