This video is part 1 of a 6 part series on matrix math. These videos are not specific
to any particular program. It is just to give you an introduction on matrices and how to
calculate them by hand. Each part will be a little bit different. Part 1 is an introduction
to matrices in general. Part 2 will be addition and subtraction in matrices. Part 3 will be
multiplication and division element by element in a matrix. Part 4 will be on matrix multiplication.
Part 5 will be on matrix transpose and the determinant. Part 6 will be on the inverse
of a matrix. A matrix is a set of data arranged in rows and column. These data are usually
numerical. For example this is matrix "A". Matrix "A" is a 3 by 4 matrix. It is called
a 3 by 4 matrix because it has 3 rows and 4 columns. If a given matrix has the same
number of rows as it does columns it is called a square matrix. This is matrix "B" which
is a 2 by 2 matrix. Square matrices are useful in that you can do specific calculation with
them that you are unable to do with other matrices. For example you can only find the
determinant of a square matrix and you can only find the inverse of a square matrix.
Here is matrix "C". Matrix "C" is a 4 by 4 square matrix. As the matrices get bigger
it becomes harder and harder to pick individual spots and refer to them in a calculation.
Each number or spot in a matrix is called an element. Each element has a location. For
example in this "C" matrix if I want to find the number 3.5 which is right here I need
to refer to its location. In this case the number 3.5 is in the second row and fourth
column which means C_2,4. That is only one way to write it. There are multiple other
ways. For example you can do C_(2,4) or C(2,4). Although my letter C is a lot like the side
of the parenthesis so it could get confusing there. With matrices there are other types
of matrices that are specific in that they have unique characteristics. For example the
identity matrix. The identity matrix is the equivalent of the number one. Any matrix that
is multiplied by the identity matrix will return the same matrix that you started with.
It is usually represented by a capital "I". There are two unique things about the identity
matrix. First is the identity matrix has to be square so it will always have the same
number of rows as columns. The second is that the identity matrix is completely filled with
0 except for a diagonal line of ones down its side. Here is 5 by 5 identity matrix.
This matrix you can see that diagonal line of 1 much easier. You can make your identity
matrix as large as you need it to be as long as it remains a square. The next type of matrix
is called a singular matrix. A singular matrix is a matrix that has no inverse. You can test
the singularity of a matrix by finding its determinant. If it has a determinant of 0
the matrix is singular. The reason you want to test a matrix to find our if it is singular
is many calculations require you to find the inverse of a matrix. If you have a matrix
that cannot have an inverse then your calculation will fail. The example given above is one
of the most common ones that you will come across. Usually you will generate a random
matrix to test any calculation you do on your computer and this will be the first one that
comes to mind however, it is a singular matrix. It will not allow you to do an inverse or
find its determinant. The inverse and the determinant will both be covered in different
videos. The final type of matrix are called vector matrices. There are two types. A row
matrix and a column matrix. They are also known as row vector and column vector. Their
characteristic is that they are only a single row or a single column as you can see here.
depending on how it is being used it will be referred to as either vector matrices.
It is different for different programming languages. Make sure with you professor which
name that they would prefer you to use when working on assignments. Normally it does not
matter as long as you understand what you are talking about and so does any one else
you are trying to explain it to.