Question

why do we use this expression to denote matrices?

https://www.dropbox.com/s/qeudrons2e9d2yt/Screenshot%202016-03-11%2020.14.15.png?dl=0


Doesn't that expression give us a single number (scalar) ? How can a matrix be represented such way?

Answer 1

are you asking about the summation with a_ij x_j ?

Answer 2

yes @phi

Answer 3

you can think of that summation as the "dot product" of row vector a with column vector x
\[ a^T x \]
you get one scalar b
but then you do that again for the next row i.e. the next "i"
you end up with M values.

Answer 4

so is the result a vector ?

Answer 5

yes, you get a vector with "b" values
it's the same as
Ax = b
where A is a matrix, x is a column vector, and b is a column vector.