# fa11_mae260_linalg1 - MAE260 Lecture 8 Linear Algebra Part...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

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

Unformatted text preview: MAE260 Lecture 8 Linear Algebra: Part I November 10, 2011 Fall 2011 MAE260 8–1 Matrices Some notations: – v ∈ R n : v is a n-dimensional vector whose entries are all real. – A ∈ R n × m : A is a m by n matrix whose entries are all real – We can also define vectors and matrices in complex domain (and the textbook is written in this domain), but for now we will focus on real vectors and matrices for which we can easily talk about their geometric meanings. I assume that everyone is familiar with matrix addition and multipli- cation – so, I will skip them. Your probably first encounter of matrices in the context of System of Linear Equations: – Example: Dad gives 1/10 of his income to his 1st kid and 1/6 to his 2nd kid, while Mon gives 1/9 of her income to the 1st kid and 1/8 to the 2nd one. Dad’s income = x D , Mom’s income = x M , 1st kid’s allowance = y 1 , and 2nd kid’s allowance = y 2 . Then, we have y 1 = 1 10 x D + 1 6 x M y 2 = 1 9 x D + 1 8 x M , which can be written as: y 1 y 2 = 1 10 1 6 1 9 1 8 x D x M – Two types of problems can be paused with the above representa- tion. – Forward problem: for given x D and x M , find y 1 and y 2 ⇒ simply matrix multiplication November 10, 2011 Fall 2011 MAE260 8–2 – Backward problem: for given y 1 and y 2 , what is appropriate x D and x M ? ⇒ linear equation solving, which have interested many people and is still a research problem. – We will revisit linear equation solving in the later part. Another encounter of matrices: coordinate transformation and/or vector rotation....
View Full Document

{[ snackBarMessage ]}

### Page1 / 9

fa11_mae260_linalg1 - MAE260 Lecture 8 Linear Algebra Part...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online