Positive definitive matrix in wikipedia

[de_student]

Hi all. I have a quick question

In this wikilink en.wikipedia.org/wiki/Positive-definite_matrix in the first example

I don't get how they get 2x1^2 -2x1x2+2x2^2-2x2x3+2x3^2 in the third line.

Can anyone bother to explain?

Thanks a lot

 

[chiro]

Hi all. I have a quick question

In this wikilink en.wikipedia.org/wiki/Positive-definite_matrix in the first example

I don't get how they get 2x1^2 -2x1x2+2x2^2-2x2x3+2x3^2 in the third line.

Can anyone bother to explain?

Thanks a lot

Hey de_student and welcome to the forums.

For that line they are multiplying a row vector by a column vector which translates to an inner product. So if the row vector is [a, b, c] and the column vector is [x, y, z]^T then the result will be ax + by + cz using the standard definition of matrix multiplication.

 

[de_student]

Hi. Thanks for prompt answer. But my question is in the example there is not always [c]-member from row vector. like there is no x3 in the member (2x1-x2). How can I deal with that?

 

[chiro]

Hi. Thanks for prompt answer. But my question is in the example there is not always [c]-member from row vector. like there is no x3 in the member (2x1-x2). How can I deal with that?

I'm not sure what you mean, but the expression has been expanded out in the right manner. The reason there is no x3 for this term is because the M matrix has a 0 element at row 3, column 1. This is why there is no x3 element for this particular case in that particular cell.