What is TR AB?
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A. The trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities), and it is invariant with respect to a change of basis.
What is meant by Idempotent Matrix?
In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix is idempotent if and only if . For this product to be defined, must necessarily be a square matrix.
How do you calculate chiller TR?
Divide Q (BTUs per hour) by 12,000 (the number of BTUs in one ton of cooling capacity). This yields the chiller capacity required to handle the process heat load in tons per hour: Example: 240,000/12,000= 20 tons/hr.
What is TR cooling capacity?
Ton of Refrigeration (TR): Ton of Refrigeration (abbreviated as TR) is an important historical unit of refrigeration capacity. Originally 1 TR was defined as the rate of heat transfer required to make 1 short ton (2000 lbs) of ice per day from water at 0oC.
Why is TR AB TR BA?
Call this corresponding b the transpose element of its a. Similarly, the (i, i) element of AB is the product of the elements of the ith row of A times their transpose elements in B. Thus Tr(AB) is the sum of each element of A times its transpose element. The sum of all these is, by definition, Tr(BA).
Is TR AB )= Tr A Tr B?
Unlike the determinant function, one does not usually have tr(AB) = tr(A) tr(B).
What is idempotent and nilpotent matrix?
Idempotent means “the second power of A (and hence every higher integer power) is equal to A”. Nilpotent means “some power of A is equal to the zero matrix”.
Is rank of AB rank of BA?
(ii) If A and B are normal, then rank(AB) = rank(BA). (iii) If A and B are Hermitian, then AB ∼ BA.