A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix.
(a) Show that I − A is also idempotent.
(b) Show that if A is invertible, then A = I.
(c) Show that the only possible eigenvalues of A are 0 and 1. (Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.)
Answers
Answer:
There is considerable confusion and misunderstanding about the meaning of the maximum reported Specific Absorption Rate (SAR) values for cell phones (and other wireless devices). SAR is a measure of the rate of RF (radiofrequency) energy absorption by the body from the source being measured – in this case, a cell phone. SAR provides a straightforward means for measuring the RF exposure characteristics of cell phones to ensure that they are within the safety guidelines set by the FCC.
Many people mistakenly assume that using a cell phone with a lower reported SAR value necessarily decreases a user’s exposure to RF emissions, or is somehow “safer” than using a cell phone with a high SAR value. While SAR values are an important tool in judging the maximum possible exposure to RF energy from a particular model of cell phone, a single SAR value does not provide sufficient information about the amount of RF exposure under typical usage conditions to reliably compare individual cell phone models. Rather, the SAR values collected by the FCC are intended only to ensure that the cell phone does not exceed the FCC’s maximum permissible exposure levels even when operating in conditions which result in the device’s highest possible – but not its typical - RF energy absorption for a user.
SAR Testing
SAR testing uses standardized models of the human head and body that are filled with liquids that simulate the RF absorption characteristics of different human tissues. In order to determine compliance, each cell phone is tested while operating at its highest power level in all the frequency bands in which it operates, and in various specific positions against the dummy head and body, to simulate the way different users’ typically hold a cell phone, including to each side of the head. To test cell phones for SAR compliance, the phone is precisely placed in various common positions next to the head and body, and a robotic probe takes a series of measurements of the electric field at specific pinpoint locations in a very precise, grid-like pattern within the dummy head and torso. All data for each phone placement are submitted as a part of the equipment approval test report for final authorization. However, only the highest SAR values for each frequency band are included in the final authorization to demonstrate compliance with the FCC’s RF guidelines.
Answer:
Step-by-step explanation: