Notation in Hoffman and Kunze's Linear Algebra

In summary, the conversation discusses the notation A(i,j) used in Hoffman and Kunze's Linear Algebra textbook. The notation refers to the ij'th entry of a matrix A and is used to make a subscript on an index more readable. The problem referenced is on page 149 and the notation is also seen on page 142, but there is no definition provided. A helpful reader suggests that the notation A(j_1,k_1) is equivalent to A_{j_1k_1} in order to make the double subscripts easier to read.
  • #1
Jolb
419
29
I'm in a class that uses Hoffman and Kunze's Linear Algebra, and I've been assigned a problem where I can't figure out their notation.

The notation is A(i,j). A is a matrix. What does this mean?

It doesn't mean the i,j entry in A [that's A with subscripts i,j] and it's not the matrix A with row i and column j removed [that's A(i|j)].

Could somebody tell me what A(i,j) means?
 
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  • #2
There's a discussion (eq 2-18 in the version I have) where they use the notation R(i,j) for the ij'th entry of a matrix. I think they did it to make a subscript on an index more readable. If there's still a confusion you might want to explain the context in which they're using that notation and/or a page reference.
 
  • #3
The book I'm using is 2nd edition.

The problem is on p. 149 and the other place I've spotted it is on p. 142. Neither place has a definition...Edit:

I see your reference (p.56). Thanks for your help!
 
  • #4
It looks like

[tex]A(j_1,k_1) = A_{j_1k_1}[/tex]

and they decided to use that notation because the double subscripts on the RHS are small and hard to read.
 

1. What is the purpose of notation in Hoffman and Kunze's Linear Algebra?

The purpose of notation in Hoffman and Kunze's Linear Algebra is to provide a standardized way of representing mathematical concepts and operations. It allows for clear and concise communication of mathematical ideas, and makes it easier to understand and manipulate complex equations and proofs.

2. How should I read and interpret the symbols in Hoffman and Kunze's Linear Algebra?

The symbols in Hoffman and Kunze's Linear Algebra should be read and interpreted according to the conventions and definitions provided in the book. It is important to pay attention to the context and use of the symbols, as they may have different meanings in different sections or chapters.

3. Are there any common mistakes to avoid when using notation in Hoffman and Kunze's Linear Algebra?

Some common mistakes to avoid when using notation in Hoffman and Kunze's Linear Algebra include using symbols inconsistently, misinterpreting symbols, and not following the proper order of operations. It is important to carefully read and understand the notation conventions in order to avoid these mistakes.

4. Can I use my own notation when working with Hoffman and Kunze's Linear Algebra?

While it is possible to use your own notation when working with Hoffman and Kunze's Linear Algebra, it is generally recommended to stick to the notation used in the book. This ensures consistency and makes it easier for others to understand your work. If you do choose to use your own notation, it is important to clearly define and explain it to avoid confusion.

5. How can I improve my understanding of notation in Hoffman and Kunze's Linear Algebra?

To improve your understanding of notation in Hoffman and Kunze's Linear Algebra, it is important to practice using it in various problems and proofs. You can also refer to the examples and exercises in the book, and seek help from your peers or instructor if you are struggling with a particular notation. Additionally, reviewing and revisiting the notation conventions regularly can help reinforce your understanding.

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