May 16, 2020 · This definition works for linear functions but I was asking more about the specific term "linear" and how you would approach it regardless of what comes after the word linear, whether it be …

Sep 8, 2011 · We get the name 'linear' from the prototypical example of a linear function in one dimension: a straight line through the origin. However, linear functions can be more complex than …

May 15, 2019 · Where is the reference to a straight line? So, whether linear is just a word used in different contexts? Does it have different meaning in different situation? Or linearity refers to some …

Oct 7, 2012 · What is the difference between a linear and a 'non-linear' space. I am starting a self-study of linear algebra so this word is extremely important, but what exactly does it mean (especially in …

Linear algebra is linear because it is the study of linear functions on vector spaces (at its root anyway). A matrix actually is a linear map (and vice versa for finite dimensional spaces).

I have a very hard time remembering which is which between linear independence and linear dependence... that is, if I am asked to specify whether a set of vectors are linearly dependent or …

Dec 22, 2020 · I have encountered this when referencing subsets and vector subspaces. For example, T ⊊ span(S) should mean that T is smaller than span(S)--at least from what I've gathered. Is ⊊ a sort of …

Sep 24, 2023 · A matrix can be defined as a rectangular array of numbers, but that is to miss the reason that matrices are so important. A matrix is a representation of a linear mapping with respect to a …

Nov 8, 2016 · For example, for the homogeneous linear equation 7x + 3y − 10z = 0 7 x + 3 y 10 z = 0 it might be a trivial affair to find/verify that (1, 1, 1) (1, 1, 1) is a solution. But the term trivial solution is …

The way that this is done in linear algebra classes is with Gaussian elimination: a basis for the column space of A A is given by the columns of A A which become pivot columns in the echelon form of A A. …