What is the size of the matrix: [itex]={\bf x}{\bf x}^T\,?[/itex]devonho said:Homework Statement
Hi,
Is there a matrix property that can be applied to take the square of a column vector?
Something like:
[itex]{\bf x}=\left[x_1,x_2,x_3\right]^T[/itex]
[itex]\left[{\bf x}\right]^2[/itex]
[itex]={\bf x}{\bf x}^T[/itex]
or
[itex]={\bf x}^T{\bf x}[/itex]?
Thank you.
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A column vector is a type of mathematical notation used to represent a list of numbers or variables arranged in a vertical column. It is often used in linear algebra and is denoted by a bold lowercase letter with a single column of numbers or variables beneath it.
A column vector is different from a row vector in terms of its orientation. A column vector has a single column of numbers or variables, while a row vector has a single row. In other words, a column vector is written vertically, while a row vector is written horizontally.
Squaring a column vector means multiplying each element in the vector by itself. This can also be thought of as finding the dot product of the vector with itself. The result of squaring a column vector is another column vector with the same number of elements, where each element is squared.
The square of a column vector is represented by raising the vector to the power of 2, denoted by a superscript 2. For example, if we have a column vector v, its square would be represented as v2. This indicates that each element in the original vector has been squared.
Squaring a column vector is often used in mathematical calculations and equations, particularly in linear algebra and vector calculus. It can also be used to represent certain physical quantities, such as velocity or acceleration, that have both magnitude and direction.