Many recent investigations have dealt with the quantity $\sca{u}$, the number of occurrences of a word $u$ as a scattered subword of a word $w$. The quantity gives important numerical information about the word $w$. Sufficiently many values $\sca{u}$, for different $u$'s, characterize the word $w$ completely. Certain upper triangular matrices, often referred to as {\em Parikh matrices} have turned out to be very useful for computing numbers $\sca{u}$. In this paper we discuss some properties of Parikh matrices, as well as some criteria concerning matrix equivalence of words. Special emphasis is on the so-called {\em Cauchy inequality} for words.