Lecture 9 Flashcards
What is a second way of writing the dot product of two vectors be written as?
u * v = u^Tv
What is cos 90 equal to?
0
If the angle between two vectors is 90 degrees, what is their dot product?
0
What does it mean if two vectors are orthogonal?
the angle between the two vectors is 90 which means they are perpendicular
What is the sum of two vectors u and v in R^n?
the element-wise sum of their components
What happens if c is a scalar and we multiply it with v?
we will just have to multiple every element in the column by c
What is a linear combination of v_1, v_2, …, v_d?
a_1v_1 + a_2v_2 + … + a_dv_d where a_1, a_2, …, a_d are all scalars
What is a span?
the set of all vectors that can be created using linear combinations of those vectors
What vector in span(x) is closest to y?
the orthogonal projection of y onto span(x)
What is the projection error?
e = y - wx
What is the definition of the projection error?
the vector that connects y to span(x)
How would we make e as short as possible?
finding an e that is orthogonal to wx
What vector in span(x) is closest to y?
w* = x * y /x * x
What do we call w*x?
the orthogonal projection of y onto span(x)
