What is column vector?

A column vector is a matrix with a single column and multiple rows. Each entry of the vector represents one element of the underlying mathematical system, such as real or complex numbers. Column vectors are commonly used in linear algebra to represent a system of linear equations or to describe vector spaces.

The elements of a column vector can be added or subtracted according to the usual rules of arithmetic. Scalar multiplication involves multiplying each element of the vector by a constant factor. Column vectors can be added or subtracted if they have the same number of rows, and they can be multiplied by a matrix if the number of columns in the matrix matches the number of rows in the vector.

Column vectors are also used to represent transformations in geometry, such as translations, reflections, and rotations. They are useful for representing forces and velocities in physics, and for representing quantities such as prices, quantities, and temperatures in economics.

Overall, column vectors are a fundamental tool for understanding and analyzing mathematical and scientific concepts in a wide range of fields, from physics and engineering to finance and economics.