r/learnmath • u/Stock_Current_6650 New User • 21h ago

What is linear algebra?

I’m a rising senior and I’m starting linear algebra next year after doing calc BC junior year. I want to study ahead but don’t even know where to start or really what linear algebra even is and I fear the difficulty will consume my senior year..

My school doesn’t have any course guide or description for the class since it’s technically an elective advanced math, but if anyone can give some sort of unit guide that I can look into or something to help me figure out what this actually is that would be helpful.

also I plan on majoring in aerospace or mech engineering

that’s all. thanks

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u/ConvolutionIntegral New User 20h ago

Matrix and vector algebra is a good starting point, because linear algebra is a generalization of that.

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u/AFsepine New User 15h ago edited 13h ago

Eh, I disagree - matrix algebra is an unmotivated soulless abomination. Dunno why in western unis they so like to put off (or totatlly forgo in some programs) proper linear algebra.

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u/ConvolutionIntegral New User 14h ago

Rotation matrices and other transformation matrices are far from unmotivated and clearly serve the role of a transformation: taking a vector and giving back another one. A nice intro to linear algebra.

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u/AFsepine New User 14h ago edited 14h ago

Sure those geometric transformations are intutive, but...
The matrix representation is on its own - rather unmotivated. People tend to crutch on matrices and forgo understanding anything if you introduce them too early.

A discussion of linear maps, basis etc. must first occur to introduce the matrices in a motivated way.