Next: Homework 2
Due date: September 28
Please email the graphics for problem 3 to me with the subject line
stat6341 homework 1. Problems 1 and 2 can be turned in handwritten on paper. If you
wish to include graphics in a document such as Word, please save your document as a pdf file and
email that, not the Word file.
- Show that if A is a square matrix and is nonsingular, then A
is nonsingular. Hint: use the SVD.
- Let S be an matrix with . Show that I-S is
nonsingular and that
is orthogonal. Hint: first
show that is nonsingular. Then show and use the fact that
- The file
contains stellar magnitudes (luminosity) and log(period) for a family of variable
stars called Cepheid variables in the Small Magellenic Cloud. The first column of this file gives
IDs for the Cepheids and so can be used as row names. These variable stars are important to
astronomers because the periods of their variability (logPeriod) are directly related to
their luminosity. This enables astronomers to estimate distances of these stars from their periods.
Two types of Cepheids are contained in this data set, FU and FO, and these types have slightly
different period-luminosity relationships. Note: stellar magnitudes are reversed in the
sense that higher value for magnitude corresponds to a dimmer star.
- Construct a plot of infra-red luminosity (I) vs logPeriod that uses
different colors for the two types of Cepheids. Include an informative title and a legend that
shows which color is assigned to which type.
- Construct a pairs plot of I,V,B,logPeriod that uses different colors for
Cepheid types. Include an informative title.
- Construct a graphic that show how infra-red luminosity differs between types. Repeat
for visual (V), blue (B), and logPeriod.
Next: Homework 2