Yes, it is possible for a function to have a negative semidefinite Hessian matrix at a critical point.
Yes, it is possible for a matrix to be a Hessian that is not negative semidefinite.
Yes, it is possible for the real interest rate to be negative. This can occur when the nominal interest rate is lower than the inflation rate, resulting in a negative real return on an investment.
Yes, it is possible for marginal utility to be negative in economic theory. This occurs when consuming an additional unit of a good or service decreases overall satisfaction or utility.
Yes, it is possible for the marginal product of capital to be negative in an economic context. This occurs when adding more capital to the production process leads to a decrease in output, indicating inefficiency or diminishing returns.
No because that would mean the lender was paying someone to borrow from them and they couldn't stay in business like that.
Yes, it is possible for a matrix to be a Hessian that is not negative semidefinite.
yes, it is possible to have a negative decimal.
No. The range of the exponential (antilog) function is the positive reals (unless you are dealing with the complex field).
Yes, it is possible for the inner product to be negative.
Find the range of a function by substituting the highest domain possible and the lowest domain possible into the function. There, you will find the highest and lowest range. Then, you should check all the possible cases in the function where a number could be divided by 0 or a negative number could be square rooted. Remove these numbers from the range. A good way to check to see if you have the correct range is to graph the function (within the domain, of course).
A function cannot be a probability mass function (PMF) if it violates the properties of a PMF. A PMF must assign a non-negative probability to each possible outcome of a discrete random variable, and the sum of probabilities for all possible outcomes must be equal to 1. If a function does not satisfy these properties, it cannot be considered a PMF.
Yes it is possible...
Yes, it is possible for there to be negative pressure in a closed system.
Yes, it is possible for velocity to be negative. Negative velocity indicates that an object is moving in the opposite direction of its positive velocity.
No, it is not possible for the specific heat of a substance to have a negative value.
No.
Impossible.