linear algebra - How to check the linearity of a function ...
You can find the properties for linear functions on wikipedia. for f(x) = x+4, do: f(ax) = ax + 4 != a*f(x) = ax+4a. which violates the property of linear function, so it is not a linear. for f(x) = 5, it is similar. I'm not sure about what is a fine function.
What is the equation for a 3D line? - Mathematics Stack Exchange
2013年5月28日 · $\begingroup$ t is an index of step from xo,yo,zo to xn,yn,zn ... as this is an typical stepping function. If you calculate t you will find at which fraction of the line (a,b,c) -> (x0,y0,z0) is point with coordinates (x,y,z) $\endgroup$
Converting absolute value program into linear program
Otherwise, you end up with an unbounded objective function, and the problem must be solved by other methods, e.g. mixed integer-linear programming. (If I knew this before, I had forgotten. Thanks to Discretelizard for pointing this out to me.)
What is the difference between linear and affine function?
2023年6月8日 · A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so while the linear part fixes the origin, the translation can map it somewhere else.
algebra precalculus - Is constant function also a linear function ...
2017年10月30日 · The difference in viewpoints is that the more advanced viewpoint views a constant function as a special kind of linear function, while the more elementary viewpoint views the linear functions as going beyond the constant functions by no longer having horizontal graphs. Similarly with circles and ovals.
linear algebra - How to know if a function is linearly independent …
2019年8月14日 · $\begingroup$ If there is a constant linear dependence between the functions, it also occurs between their derivatives and between their second derivatives. So assume a constant linear dependence, and evaluate the functions, their derivatives and second derivatives, at $0$. $\endgroup$ –
linear algebra - "Well defined" function - What does it mean ...
2023年5月10日 · All functions are well-defined; but when we define a function, we don't always know (without doing some work) that our definition really does give us a function. We say the function (or, more precisely, the specification of the function) is 'well-defined' if it does.
terminology - What does 'linear' mean in Linear Algebra?
2011年9月8日 · Peano used linear systems for what we now call vector spaces. This reflects the view that linear algebra is about spaces of linear algebraic relations. (p. 265, 266) Pincherle was the first to use the term linear space for the concept of vector space. (p. 270) Hahn used linear space for normed vector space. (p. 277)
real analysis - What is a "linear function" in the context of ...
2018年12月14日 · A linear function in this context is a map $f: \mathbb{R}^n \to \mathbb{R}^m$ such that the following conditions hold:
Is the absolute value function a linear function?
2015年5月20日 · I would simply define a linear function as always having the same slope (and, more technically, it must be continuous). Clearly, the absolute value function has a negative slope for values < 0 and positive slope for values > 0. So it's not linear.