Vectors and matrices are important concepts in linear algebra, a branch of mathematics. Let's break them down in a simple way.
-
Vectors:
- Think of vectors as lists of numbers.
- They can be shown in two forms: column vectors and row vectors.
- For example, a column vector looks like this:
[
v = \begin{bmatrix} a \ b \ c \end{bmatrix}
]
This is a matrix with just one column and multiple rows.
- A row vector, on the other hand, looks like this:
[
u = \begin{bmatrix} d & e & f \end{bmatrix}
]
This is a matrix with one row and multiple columns.
- There are also special types of vectors:
- Zero vectors have all their numbers as zero.
- Unit vectors have a length of one.
-
Matrices:
- Matrices are groups of vectors lined up in rows and columns.
- They can do things to vectors, like turning or stretching them.
In short, vectors are like a special case of matrices!