Without googling, looking at your notes, or reading other posts in this thread.
Basic algebra is simply using variables and operations sum and multiplication.
But in the term "Linear Algebra";
what does the "Linear" mean?
(This is one of my favorite questions to humiliate engineers)
linear spaces, linear maps----lines and planes and sheeit.
Linear algebra = algebra of linear objects and actions
>defining "linear" using the word "linear"
Enginerds spotted. Bazinga! Elon Musk! Big data! Handpicked parameters!
straight line nigger
>what does the "Linear" mean?
cA(v+w) = A(cv)+A(cw)
/this
y=mx+b
Pretty simple really
>pic: I'm glad could help
Solving linear matrices, none of the variables are multiplied by another, but they're all separated
like affine but through 0
So none of you can explain to me what LINEAR means? How terribly unfortunate. But I guess you know Justin Biebers top songs, names of Kim Kardashians dogs, and other important things in your daily strug- I mean life
y=mx + b isn't a linear function though.
linear is f(x) + f(y) = f(x + y) and f(cx) = c(fx).
>(This is one of my favorite questions to humiliate engineers)
Wouldn't they be pretty likely to know it, at least electrical engineers and such? I don't know about civil/mech/etc though.
Nice dude
It's the study of algebras generated by linear transformations, my nigga.
linear algebra is not just the study of algebras of linear maps.
linear algebra deals with linear combinations of variables. within an expression, variables are added and subtracted; there's no exponentiation or terms consisting of the product of multiple variables.
So you're saying that
f (mx) + f (b) =/= f (mx+b)?
And that y=c (mx+b) =/= cmx + cb?
f(x) = mx+b
>f(mx) = m(mx)+b
>f(b) = m(b)+b
f(mx)+f(b) = m(mx)+b + m(b)+b = m(mx+b) + 2b
f(mx+b) = m(mx+b) + b
>f(mx) + f(b) = f(mx+b)
is the same as saying
>m(mx+b) + 2b = m(mx+b) + b
>2b = b
Basic stuff. A middle schooler could've checked you.
"Linear" is usually used to describe types of functions. Functions that satisfy the identity f(a*x + b) = a*f(x) + b (of course, this definition can be expanded to multiple different independent variables). "Linear" can also be used to describe the concept of "linear combinations," in which one takes a set of elements, multiplies each of the elements by a coefficient, and then adds the product up. There is also the concept of linear differential equations, where one can solve the equation by creating many additional differential equations, and by modeling the differentiation operation via multiplication by a matrix. Specifically, the matrix undergoes a change of basis based on its eigenvectors, which can be trivially solved with the exponential function.
means 1st degree polynomials?
No user, they're defining a term with linear in it using linear. Like defining a black hat as a covering for your head that happens to be black.
This is the correct answer in this thread.
Note that a transformation is considered linear if:
T(ax + by) = aT(x) + bT(y), where a, b are constants.
This is typically what is meant by "linearity." Also, linear algebra is usually one's first exposure to abstract algebra and matrix theory.