Equation (9.138) for the signal-to-noise ratio (SNR) of a vector

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Equation (9.138) for the signal-to-noise ratio (SNR) of a vector

Equation (9.138) for the signal-to-noise ratio (SNR) of a vector quantizer includes the SNR formula of Equation (3.33) for standard pulse-code modulation as a special case for which k = 1. Justify the validity of this inclusion.