Actually, the only constant function that is linear is the 0 function. If you have a linear map T:V-->W between V.Spaces (this generalizes to rings, etc.) then, if T(v)==wo , i.e., T(v)=wo for all v in V, then: T(v+v')=wo≠ T(v)+T(v')=wo+wo=2wo. A similar argument applies to maps from a vector space to its base field.
well then i dont know what a constant and nonconstant linear functions are. Because f(x)=x is linear when graphed, so i was assuming linear is synonymous the word constant. as in a constant rate of change or constant slope.
A constant function is a function which always takes the same value, for example f(x)=2. All linear functions on R^{n}can be written as y=Ax where A is a matrix (in one dimension, just a number)
spoke: You may be confusing constant rate of change, i.e., constant derivative--a property of linear functions-- with constant function.
Yes, exactly, that is what a constant function is like when seen as a subset of AxB. Not to nitpick, but you may want to specify the sets A,B where you are defining your function as a subset of AxB; here, A is clearly specified, but it is not clear what B is (unless you assume your function is onto B).
A linear function is constant if and only if its slope is zero. By contaposition, a linear function is not constant (i.e. non-constant) iff its slope is different from zero.
Your right, Dickfore, but your example is that of a map from ℝ to itself may be too specific for a general definition of function.
OK, make [tex] \mathbf{y}_{n \times 1} = \hat{A}_{n \times m} \cdot \mathbf{x}_{m \times 1} + \mathbf{b}_{n \times 1} [/tex] This is a general mapping from [itex]\mathbb{C}^m \rightarrow \mathbb{C}^n[/itex]. But, now, the function may be constant in a more general case, when [itex]\mathrm{rank}A \le m < n[/itex].