lecture_E7_12

# lecture_E7_12 - Lecture 12&13 linear equations Linear...

• Notes
• 42

This preview shows pages 1–11. Sign up to view the full content.

Linear equations, linear functions Engineering (physical) interpretation of linear equations Problem of inversion Determinants Inversion (square matrices) Independence of vectors Range of a matrix Null space of a matrix Lecture 12 &13: linear equations Reference: book, Chapter 6 Additional material: Lecture_12_***.m (available on bSpace) Steven Boyd, Stanford University, EE263

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

Linear equations Example of linear equations (Chap. 6, p. 365) Which can be written in matrix form Or more symbolically as: Where
Linear equations Linear equations: Can be written in matrix form: Or alternatively in compact form

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

Example of linear equations Linear circuit (example book, Chapter 6, page 370) Equations for voltages and intensities are linear In the following equation, if you know the voltages, the intensities can be obtained by solving the following linear system where the unknown are the currents i’s
What is a linear function? Let be a function. It is said to be linear if This is sometimes called superposition

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

Matrix representation of a linear function
Interpretation of

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

Interpretation of
Problem of inversion If all quantities involved were numbers, solving the following problem i.e. finding as a function of and Could formally be written as Of course, the definition of the “inverse”, or “one over” the matrix has to be defined properly, and the conditions in which it is legal for the inverse to exist need to be defined as well.

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

Determinants (square matrices) Consider a square 2 x 2 matrix The determinant of the square matrix is The determinant of a general n x n square matrix is a nonlinear operation which results in a polynomial in the coefficients of the matrix.
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