LA 4.3

Main Points: When two values, x and y, that are proportional to each other but do not have equal constant values, the points are not found on the same line. However, a multiple of x can reach the closest to the y value, and this is called the projection of y on the line spanned by x. The step from x to y is caleld the residual vector, r. Because the residual vector and the quantity mx (the multiple of x) are perpendicular, the vectors equal 0. To solve for y, the dot product is necessary. The line y=mx is called the least squares fit to the data. Curve-fitting with two parameters leads to projections onto 2-dimensional subspaces. Scatter plots are used to collect data in order to find the values of m,a, and b in the equation s=ma +b. Finding the linear combination that is closest to s allows us to approximate the answer. Least-squares curve-fitting with J parameters leads to projection onto subspaces spanned by J vectors. The residual vector is perpendicular to all of the vectors in the set.

Challenges: I'm very confused about the J area of the LA. I really don't understand what J actually is or what it stands for. Also, I was confused on why the LA solved the equation in 4.3.1 the way that it did.

Reflections: This reading seemed to add onto what we were doing in class on Thursday. Even though I didn't fully understand the material, I think it will be more helpful in continuing what we were learning from the lecture on Thursday.

Reflections: