In Leigh's double lesson of Maths and Logic fundamentals, we looked at Matrices.
Matrices are a container or array of numbers. In other words, it's a set of numbers contained within a set. It's a mathematical and (very) technical method of producing arrays in programming.
The applications of matrices are found in most scientific fields. In every branch of physics, including classical, mechanics, optics, electromagnetism etc.
What does a matrix look like?
A i, j. The 'i' represents as row and the 'j' represents as a column.
Essentially, this is what the table would look like.
A 1,1 A 1,2 A 1,3
A 2,1 A 2,2 A 2,3
A 3,1 A 3,2 A 3,3
The size of a matrix is defined by the number of rows and columns that it contains. A matrix with M rows and N columns
They can be in any given size, they don't have to be specific.
The definitive examples of matrix tables are 3 x 3 matrix (or square matrix) 3 x 1 (or column vector) 1 x 3 Matrix (or row vector) 3 x 4 Matrix (or rectangular matrix)
A unit that is within a table for the row and columns are considered as an element (or entry) (coordinates are represented as i and j, subscripts, e.g)
Matrices can be added when they share the same number of rows and columns.
I will go over the principles and rules of matrices.
Addition
Addition uses commutative rules, we can say that A+B = B+A because they're both the same. Consider this as an establishment of a rule or system rather than having any actual applied use.
Example:
Subtraction
We can't use the commutative rule here because A - B doesn't equal the same as B - A
Consider this as an establishment of a rule or system rather than having any actual applied use.
Example:
Multiplication: 01 Scalar multiplication
Scalar multiplications can scale something by multiplying the number with another number. It can be done in 2 ways. In one method, a letter has to be a lower case and the other letter has to be an upper case. Lower case only consists of one number was an upper case contains a set of numbers. You times them both together based on how many times you can do so. The second method is a Scalar diagram. You produce as many dots and lines you can fit in.
Multiplication: 02 Multiplication
Multiplication is when your multiplying two matrix values. One value is in a set of numbers and the other applies the same. Except this time, both are upper case meaning they both have a set of numbers/values.
Negative Matrices:
Whenever negative matrices occur you would simply reverse the sign of elements within. So if you had one row which was a negative set of numbers and the other row has postive set of numbers. You flip them and change the A to -A
Matrices and Algebraic applications:
The elements of a matrix don't need to be numbers. It can be letters, functions, equation etc. Those kinds of questions will occur when you get 2 rows worth of numbers and will
result in something at the end of it.
And that all wraps up for this blog!
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