Anton speaks French and German Geraldine speaks English Fren

Anton speaks French and German; Geraldine speaks English, French and Italian; ...

I think I\'m good with the matrices. Please help with the, \"Explain the significance of the matrices AAT and ATA.\" part. I\'m ot sure what they\'re looking for. Also, please forgive me if this isn\'t the correct math category. It\'s for a Diff Eq w/Linear Algebra class and Linear Algebra isn\'t an option to select.

Solution

Matrix AA^t represents the corellation between Anton, Geraldine, James and Lauren with respect to what languages they speak. It basically represents how many languages are common to any of these people. For example:

a11 = Anton and Anton: There are two common languages (French and German)

a12 = Anton and Geraldine: There is one common language (French)

a13 = Anton and James: There is common language (because French and German, however James speaks English and Spanish)

Likewise all the entries of matrix AA^T represent common language spoken by corresponding people.

Same way A^tA represents correlation between any set of languages, depending upon how many people speak those langauges.

For exmaple:

a11= French and French: French is spoken by two people (Anton and Geraldine)

a12 = French and German: French and German are spoken by one person (Anton)

a13 = French and English: French and English are spoken by one person (Geraldine)

Similarly all the entries of A^tA represents the number of people who speak common tongues.