query: Different Definitions of Linear Functions?
positive_passages.docid: 17158
positive_passages.text: Definitions of "linearity" across branches of mathematics or levels of math education
negative_passages.docid: 157844
negative_passages.text: If $f: \mathbb{C} \to \mathbb{C}$ is analytic and not linear, then $z, f(z), f(f(z)), \dots$ are linearly independent functions over $\mathbb{C}.$
negative_passages.docid: 96354
negative_passages.text: Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
negative_passages.docid: 137873
negative_passages.text: Problems that involves two facts in the definition of vector spaces
negative_passages.docid: 11169
negative_passages.text: Semantic meaning of writing functions
negative_passages.docid: 131786
negative_passages.text: Why are second order linear PDEs classified as either elliptic, hyperbolic or parabolic?
negative_passages.docid: 28740
negative_passages.text: How to know the usage of undocumented function like LinearAlgebra`BLAS?
negative_passages.docid: 3810
negative_passages.text: When is a function a dimension?
negative_passages.docid: 121464
negative_passages.text: Linearized equations
negative_passages.docid: 116881
negative_passages.text: Why is a linear transformation called linear?
negative_passages.docid: 55420
negative_passages.text: How does the chain rule work for functions from vectors to vectors?
negative_passages.docid: 64041
negative_passages.text: Difference between functional and function.
negative_passages.docid: 152781
negative_passages.text: Chain rule for multivariable functions confusion
negative_passages.docid: 75266
negative_passages.text: $f(a+b)=f(a)+f(b)$ but $f$ is not linear
negative_passages.docid: 142873
negative_passages.text: What does the function f: x ↦ y mean?
negative_passages.docid: 10181
negative_passages.text: Entire one-to-one functions are linear
negative_passages.docid: 71807
negative_passages.text: Defining a function by equations with different number of arguments