Matrices (Pt. 1): Intro
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Matrix represents the bulk of our discussion as all possible discussed entities are arguably matrices with varying sizes.
Matrices are expressed through rows by cols, with
m x n (read as m by n)
3 x 2 (read as 3 by 2)
Type
Size
Example
Matrix
m x n
[1, 2, 3]
[4, 5, 6]
Square Matrix
n x n
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]
It may though be superficial, but what distinguishes between a vector or a matrix is that both m and n variables has to be greater than 1.
An element (or item) of a matrix is conventionally referred to by its location with
i being its row number, while
j being its column number
Hence, for Matrix "a" is particular, we could reference an element by calling for example "a one-two".
The following operations can be read at face-value. For example, Matrix-"some-entity" "some-operation" .
Scalar-value is applied to all elements of the matrix.
Scalar-value of each elements are applied to respective elements of matrices.
Matrices must be of the same size
Matrices can undergo addition, subtraction, and mostly multiplication, but never division (lol) .