#Linear Algebra

38 messages · Page 1 of 1 (latest)

cosmic quartz
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So i want to self teach myself linear Algebra before i start it, what should i begin with? And what are the prequisites for it?

cloud canyon
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the ones I have start with vectors and matrices, mostly

cosmic quartz
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So basically vectors and matrices right?

cloud canyon
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I'll tell you the contents of a book I have, sec

cosmic quartz
cloud canyon
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So, these are the chapter of the book. Sadly, it's in german so you'll habe to translate it using an app.

IMG_20250902_232315.jpg IMG_20250902_232341.jpg IMG_20250902_232347.jpg IMG_20250902_232400.jpg
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I know it's a bit inconvenient, but I didn't want to translate the chapter names only and have you scrambling for stuff

open beacon
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My understanding is that the reason it's called "linear algebra" is because it's about using the techniques of algebra to study linear transformations.

cloud canyon
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Ofc this won't list everything as well (It's Linear algebra 1)

outer copper
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Ive heard good things about a book called linear algebra done right

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But ive never used a book for lin alg tbh

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Why do i keep seeing 108 typing just say what u have to say (:

cloud canyon
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Eh whatever

  1. Sets and images
    1.1 Sets
    1.2 Images

  2. Vector spaces
    2.1 Real vector space
    2.2 Complex numbers and complex vector spaces
    2.3 linear subspaces
    2.5 fields

  3. Dimensions
    3.1 Linear independece
    3.2 Meaning of the term "dimension"
    3.5 Vector product/Cross product

  4. Linear maps
    4.1 Linear maps
    4.2 Matrices
    4.4 Quotient spaces
    4.5 Rotations and reflection in R²

  5. Calculating using matrices
    5.1 Multiplication
    5.2 Rank of a matrix
    5.3 Elementary linear transformation
    5.5 How do you invert a matrix?

  6. The determinant
    6.1. The determinant
    6.2 Calculation of determinants
    6.3 The determinant of a transposed matrix
    6.4 A formula for the determinant of an inverted matrix
    6.5 Determinant and matrix product
    6.7 Determinant of an endomorphism
    6.8 Leibniz' formula

  7. Linear systems of equations
    7.1 Linear systems of equations
    7.2 Cramer's rules
    7.3 Gaussian elimination

  8. Euclidean vector spaces
    8.1 Scalar products
    8.2 Orthogonal vectors
    8.3 Orthogonal projections
    8.4 Groups

  9. Eigenvalue
    9.1 Eigenvalue of a vector
    9.2 The characteristic polynomial
    9.4 Polynomials

  10. Diagonalization
    10.1 Self-adjoint endomorphisms
    10.2 Symmetrical matrices
    10.3 Diagonalization

  11. Classification of matrices
    11.1 What does "classifying" mean?
    11.2 Rank of a matrix
    11.3 Jordan normal form
    11.4 Diagonalization, again
    11.5 Sylvester's law of inertia

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.
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Left out the unnecessary or vague stuff
A few words may be incorrectly translated as well

cloud canyon
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I lost 9 of my fingers in a freak Play-Doh accident 14 years ago.

outer copper
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ur book sounds so boring actually

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have you been enjoying it at all?

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i think i enjoyed learning linear algebra but it can be really repetitive

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(diagonalization is my worst enemy)

outer copper
cloud canyon
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Noticed a bit too late

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Sometimes he'll explain things using graphics, which don't really make sense

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For example the image or preimage of a function

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Asked my highschool maths professor about it a few years ago too, to which he told me that "this explanation makes no sense"

cosmic quartz
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Sorry I was gone

cosmic quartz
cosmic quartz
cloud canyon
cosmic quartz
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It contains what I asked for

cloud canyon
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You might really want to check out some other books though

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and see how others did it

cosmic quartz
shrewd thorn
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Check out Linear Algebra by Friedberg Insel Spence