What does multiplying a vector mean?
Scaling one vector and combining two vectors are different operations. Check the operands and the type of result before interpreting the notation.
Read on through a shared source
What do the numbers in a vector describe? →Translate between an arrow and a list of coordinates. Each representation makes a different aspect of the same object easier to inspect.What is geometric about a word embedding? →Coordinates describe a vector relative to a basis. Embeddings use learned vectors whose directions can capture relationships among words.How can columns explain a matrix equation? →Translate coordinates into a geometric picture. The columns of a matrix then show which combinations of vectors can reach the desired output.
Compare the passages
these two fundamental operations, vector addition and scalar multiplication.multiplying two vectors together is the dot product plus the wedge product