Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What are matrix coefficients in linear algebra? And what does it mean "integer matrix coefficients"?

share|improve this question
    
If you read this term from some sentence in some literature, quoting the sentence in your question would be helpful for the readers to understand the context. –  user1551 Dec 29 '12 at 19:11
add comment

2 Answers 2

up vote 2 down vote accepted

Matrix coefficients are the entries of the matrix. Integer matrix coefficients is just a matrix with integer entries.

share|improve this answer
    
Thanks! Didn't know the definition. –  J-unior Dec 29 '12 at 18:24
    
@J-unior Glad to help. Remember you always can upvote posts which are useful to you. You can accept the answer is you consider it really answers your question. –  leo Dec 29 '12 at 18:29
    
I know, I'm not new at stackexchange. Still don't have enough rep to do this, and 10 minutes are not over yet :-) –  J-unior Dec 29 '12 at 18:31
add comment

Note: there is a big difference between the terms "matrix coefficient" and "coefficient matrix". I'll explain first what you are probably asking about:

Coefficient matrix

Suppose you have a system of equations:

$$\begin{align*} 1\cdot x_1 + 2x_2 &= 16\\ 3x_1 + 1\cdot x_2 &= 4 \\ \end{align*} \tag{1}$$

$(I)$ Then the coefficient matrix (in this case, with integer entries) corresponding to this system of linear equations in $(1)$ is:

$$M = \begin{bmatrix} 1 & 2\\ 3 & 1\\ \end{bmatrix} $$ where the entries in first column represents the coefficients of the $x_1$, and those in the second column the coefficients of $x_2$, etc..

The augmented coefficient matrix $M_a$ would include the entries in a third column which correspond to the values at the right of the equals signs in $(1)$:

$$M_a = \begin{bmatrix} 1 & 2 &\;|\; 16\\ 3 & 1 &|\; 4\;\\ \end{bmatrix} $$


Matrix coefficient

$(2)$ On the other hand, this coefficient matrix contrasts with what is meant by a matrix coefficient. (Please read more at the given linked entry from Wikipedia: what follows is a brief excerpt from that entry.)

In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group and additional data. For the case of a finite group, matrix coefficients express the action of the elements of the group in the specified representation via the entries of the corresponding matrices.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.