Notes_vectordiff

# Notes_vectordiff - Notes on differentiation involving...

• Notes
• CountAtomAardvark8837
• 3

This preview shows pages 1–2. Sign up to view the full content.

Notes on differentiation involving vectors Prabir Barooah October 26, 2009 We always follow the convention: A vector, by default, is a column vector. Therefore, a n -dimensional vector x is represented as x = x 1 x 2 . . . x n The derivative of a scalar function with respect to vector is represented as a row vector. Suppose x R n and f ( x ) R . Then d f ( x ) d x = [ f x 1 , f x 2 , ,..., f x n ] . (1) To remeber this and the subsequent conventions, think of Taylor series expansion of f around the “point” x o , which we would like to be able to write in the same manner if all quantities involved were scalars, i.e., f ( x o + δ x ) = f ( x o )+ d f ( x ) d x x 0 δ x + ...... Since the left hand side is a scalar, each term on the right hand side must be a scalar as well. Since δ x is a column vector (remember the first convention), this means the derivative d f ( x ) dx must be a row vector, so that their product is a scalar. This is the justification for the convention that d f ( x ) dx

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern