Key differences between Column-oriented Vertica & SQL dbs such as PostgreSQL?

Mathematically, suppose a matrix M and its transpose M'. I can consider M rowwise and I can consider M' rowwise. Now suppose that M1 is a PostgreSQL table and M1' its transpose. When I consider M1' rowwise, I am considering its columns -- column-oriented table?

I am trying to find words to explain Vertica to SQL developers and mathematicians.

What makes Vertica different from traditional db approaches? Is Vertica just a storage for the transposes of basic tables or is it a key-value pair storage for xetabyte of data?

What are the key differences between column-oriented dbs such as Vertica and traditional SQL dbs such as PostgreSQL?

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