Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Then all the points would be on a line that looks somethingĪ linear function.In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Same scale, so I'll do 1, 2, 3, 4, and 5. I could do 5, 10, 15, 20,Īxis right here.
Actually, I can it do a littleīit more granularly than that. So let me draw- I'll doĪ rough graph here. Increasing amounts, so we're definitely dealing withĪ non-linear function. Up by 5, so I already see that it is not constant. So let's see if our changeġ4, we go up by 3. We're just going to take that and divide it by 1. So in order for this function toīe linear, our change in y needs to be constant because The change in x's are always 1, right? We go from 1 to 2, 2 toģ, 3 to 4, 4 to 5. The change in y over the change in x always constant. In y by the change in x, and that should always Going by different values, if this went from 1 to 2 and thenĢ to 4- what you'd want to do, then, is divide the change We're dealing with a non-linear function. Here x is always changing by 1, so since x is alwaysĬhanging by 1, the change in y's have to always
Same value, you're dealing with a linear function. For example, for any one-stepĬhange in x, is the change in y always going to be 3? Is it always going to be 5? If it's always going to be the Tell them is for any given change in x, is the change Linear or non-linear? So linear functions, the way to but then the video wouldn't be making Sal's point which is how you can know that a function is linear just by looking at the table and this one is definitely not linear.įunction that contains the following points. Y = x² + 10, or if it showed the curve of a parabola with those points on it, then we would know that all the points were included. If the problem said that the function was defined by We haven't been told if x = 0 is included or x = 1/2 or x = -3Īnyway, those points in the table do lie on a parabola-we just don't know if there are any points between those. Sal only said that the function contains those points and no one tells us that there are any other points in the function. Technically, though, we don't know if this function is continuous or if it is defined by that table and only has those 5 points.
A quadratic describes the points that make a parabola. So, in each case shown in the table, y = x² + 10 and that is definitely a quadratic. In Sal's table, notice that every value of y equals 10 plus x^2
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