Book to learn Advanced Linear Algebra and Matrix Theory

Question

I am looking for a book to learn Advanced Linear Algebra and Matrix Theory in detail.

Sheldon Axler :Doesn't cover matrix theory,Hoffman,Kunze:Doesn't have many exercises and examples on each of the topics

Please suggest some alternatives

Requisites: Theorems with proofs,easy ones left to reader,Enough examples,Good Exercises(with Hints if possible)

Topics to cover:

Systems of Linear equations

Diagonalization of a square matrix

Vector Spaces

Solutions of Linear Systems: Gaussian elimination , Null Space and Range , Rank and nullity, Consistency conditions in terms of rank , General Solution of a linear system , Elementary Row and Column operations , Row Reduced Form ,Triangular Matrix Factorization

5.Important Subspaces associsted with a matrix: Range and Null space, Rank and Nullity,Rank Nullity theorem .

6.Orthogonality: Inner product, Inner product Spaces , Cauchy – Schwarz inequality , Norm , Orthogonality , Gram – Schmidt orthonormalization , Orthonormal basis , Expansion in terms of orthonormal basis – Fourier series , Orthogonal complement.

7.Eigenvalues and Eigenvectors

Hermitian Matrices:Real symmetric and Hermitian Matrices Properties of eigenvalues and eigenvectors.

9.General Matrices: The matrices $AA^T,A^TA$ Rank, Nullity, Range and Null Space of $AA^T,A^TA$ ,Singular Value Decomposition.

10.Jordan Cnonical form: Primary Decomposition Theorem Nilpotent matrices Canonical form for a nilpotent matrix

Mostly results on MSE said to follow Matrix Analysis-Horn,Johnson but the book does not cover all the topics in great detail.It focuses on more advanced topics.

Please suggest a book accordingly as I need to prepare for my exam.

Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess. — Ben Grossmann, Oct 06 '17 at 04:55
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book. — , Oct 06 '17 at 06:46
@MorganRodgers I agree there may some things that are on his list but missing in the book but as far as I could tell a great majority of the listed items are in that book. And I think LADR is one of the most lucidly written linear algebra texts. — AnlamK, Oct 06 '17 at 13:42
Does this answer your question? High-level linear algebra book — user1147844, Apr 09 '23 at 16:31

Pietro Paparella · Answer 1 · 2023-06-25T04:40:04.950

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I highly recommend A Second Course in Linear Algebra, by Garcia and Horn.

Reviews by:

the MAA; and
Nicholas Higham.

EDIT: The second-edition is now titled Matrix Mathematics: A Second Course in Linear Algebra.

edited Jun 25 '23 at 04:40

answered Dec 20 '18 at 18:48

Pietro Paparella

3,500
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score 3 · Accepted Answer · answered Sep 12 '21 at 17:29

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I loved Linear Algebra by Friedberg Insel and Spence

The book by Lax is also excellent.

answered Sep 12 '21 at 17:29

NicNic8

6,951

score 0 · Answer 3 · answered Dec 20 '18 at 20:02

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The Linear Algebra a Beginning Graduate Student Ought to Know has a pretty good presentation of all this material. It's got some less standard notations and terminology, but it's a good, detailed look at advanced linear algebra and matrix theory.

answered Dec 20 '18 at 20:02

Alex Jones

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Book to learn Advanced Linear Algebra and Matrix Theory

3 Answers3

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