# What's the best textbook to learn linear algebra?

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I'm looking for a textbook to learn linear algebra in my spare time. The level I'm looking for is somewhere in between IB further maths HL and undergraduate level (Kinda vague).

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#2

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I'm looking for a textbook to learn linear algebra in my spare time. The level I'm looking for is somewhere in between IB further maths HL and undergraduate level (Kinda vague).

**jk2212**)I'm looking for a textbook to learn linear algebra in my spare time. The level I'm looking for is somewhere in between IB further maths HL and undergraduate level (Kinda vague).

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#3

As long as you find something that covers these topics, you will have a good idea of Linear Algebra. You

could even learn these topics off YouTube or Wikipedia.

Elimination, LU factorisation) to solve systems of linear equations. Consistent

and independent systems, rank and homogeneous equations. Numerical methods such as the Gauss-Seidel method and numerical errors.

could even learn these topics off YouTube or Wikipedia.

**Matrices:**Introduction to matrix algebra, determinants and inverses.**Equation solving:**Using various methods (e.g. Cramers rule, GaussianElimination, LU factorisation) to solve systems of linear equations. Consistent

and independent systems, rank and homogeneous equations. Numerical methods such as the Gauss-Seidel method and numerical errors.

**Vector spaces:**Vectors, vector spaces, subspaces, linear transformations, rank-nullity theorem. Bases and orthonormality. Methods to create orthonormal bases such as the Gram-Schmidt method.**Eigenvalues and eigenvectors:**Determining eigenvalues and eigenvectors. The Cayley-Hamilton Theorem. Eigenspaces and principles of decomposition e.g. diagonalisation. Gershgorins Circle Theorem.**Practical applications:**Practical applications of linear algebra, e.g. page ranking, facial recognition, least squares.**Abstract linear algebra:**Abstract uses of the concepts such as inner product spaces and Fourier series, m group representations and complex linear algebra.
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(Original post by

As long as you find something that covers these topics, you will have a good idea of Linear Algebra. You

could even learn these topics off YouTube or Wikipedia.

Elimination, LU factorisation) to solve systems of linear equations. Consistent

and independent systems, rank and homogeneous equations. Numerical methods such as the Gauss-Seidel method and numerical errors.

**minimums_ILS_**)As long as you find something that covers these topics, you will have a good idea of Linear Algebra. You

could even learn these topics off YouTube or Wikipedia.

**Matrices:**Introduction to matrix algebra, determinants and inverses.**Equation solving:**Using various methods (e.g. Cramers rule, GaussianElimination, LU factorisation) to solve systems of linear equations. Consistent

and independent systems, rank and homogeneous equations. Numerical methods such as the Gauss-Seidel method and numerical errors.

**Vector spaces:**Vectors, vector spaces, subspaces, linear transformations, rank-nullity theorem. Bases and orthonormality. Methods to create orthonormal bases such as the Gram-Schmidt method.**Eigenvalues and eigenvectors:**Determining eigenvalues and eigenvectors. The Cayley-Hamilton Theorem. Eigenspaces and principles of decomposition e.g. diagonalisation. Gershgorins Circle Theorem.**Practical applications:**Practical applications of linear algebra, e.g. page ranking, facial recognition, least squares.**Abstract linear algebra:**Abstract uses of the concepts such as inner product spaces and Fourier series, m group representations and complex linear algebra.Cheers for the list Now I've got a clearer idea about this topic.

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#7

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Cheers for the list Now I've got a clearer idea about this topic.

**jk2212**)Cheers for the list Now I've got a clearer idea about this topic.

Linear Algebra is very useful for Optimisation as well, if you ever ran a Simplex Algorithm, you would be using Row Reduction techniques from Linear Algebra.

I did this a while back, 2010-2013, so I've forgotten most of it (other than basic matrices multiplication and addition, plus inverses etc).

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(Original post by

Those were the topics we covered at university in Linear Algebra. It is a VERY useful topic, anything involving data with multiple entries across time will use matrices. This includes a lot of econometrics (economic modelling).

Linear Algebra is very useful for Optimisation as well, if you ever ran a Simplex Algorithm, you would be using Row Reduction techniques from Linear Algebra.

I did this a while back, 2010-2013, so I've forgotten most of it (other than basic matrices multiplication and addition, plus inverses etc).

**minimums_ILS_**)Those were the topics we covered at university in Linear Algebra. It is a VERY useful topic, anything involving data with multiple entries across time will use matrices. This includes a lot of econometrics (economic modelling).

Linear Algebra is very useful for Optimisation as well, if you ever ran a Simplex Algorithm, you would be using Row Reduction techniques from Linear Algebra.

I did this a while back, 2010-2013, so I've forgotten most of it (other than basic matrices multiplication and addition, plus inverses etc).

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#9

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I'm actually trying to learn this by myself over the gap yr. It seemed really useful for physics. Can you tell me more about econometrics? I'm surprised to hear that it's also involved in human science.

**jk2212**)I'm actually trying to learn this by myself over the gap yr. It seemed really useful for physics. Can you tell me more about econometrics? I'm surprised to hear that it's also involved in human science.

Half of my masters was in econometrics (the other half in finance). I spent the first year of a PhD in economics doing advanced econometrics (which was crazy hard).

Econometrics is essentially everything you can think of to do with analysing economic data using stats.

So we do things like Ordinary Least Squares (derivation, asymptotic limits), Generalized Least Squares (generalised version of OLS, IV (instrumental variables)), Instrumental Variables (where there is unmeasurable data), Panel Data (random effect, fixed effect), Time Series (AR, MA models, ARCH, GARCH), Bootstrapping (sampling from the data), Weak Instruments etc

It's probably the most useful stuff for an economist as these days you can't just make a statement without mathematical backing.

Yes Linear Algebra will help for Physics, especially the vector stuff. Physics relies more on Calculus, so I would focus on having perfect Calculus.

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#11

I hate it when concepts are explained using mapping notation or set theory, I mean come on.

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#12

**jk2212**)

I'm looking for a textbook to learn linear algebra in my spare time. The level I'm looking for is somewhere in between IB further maths HL and undergraduate level (Kinda vague).

*Basic Linear Algebra*(by Blyth & Robertson) to be pretty useful as an introduction to the subject.

(Original post by

Looks hardcore. What is the obsession with over using mathematical notation, rather than explaining concepts using simple english.

I hate it when concepts are explained using mapping notation or set theory, I mean come on.

**minimums_ILS_**)Looks hardcore. What is the obsession with over using mathematical notation, rather than explaining concepts using simple english.

I hate it when concepts are explained using mapping notation or set theory, I mean come on.

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#13

**minimums_ILS_**)

Looks hardcore. What is the obsession with over using mathematical notation, rather than explaining concepts using simple english.

I hate it when concepts are explained using mapping notation or set theory, I mean come on.

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#14

(Original post by

We're studying maths here right?

**newblood**)We're studying maths here right?

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#15

(Original post by

And we're writing our mathematics in English, or whatever your natural language is...

**HapaxOromenon3**)And we're writing our mathematics in English, or whatever your natural language is...

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#16

(Original post by

python is

**newblood**)python is

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