A matrix is a rectangular array of values, arranged in rows and columns.
Typically denoted by bold capital letters, such as A, B, C.
The size of a matrix is expressed as rows x columns (m x n), where m is the number of rows and n is the number of columns.

a_{11} ↓ a_{21} ↓ a_{31} ↓ a_{41} \to \to \to \to a_{12} ↓ a_{22} ↓ a_{32} ↓ a_{42} \to \to \to \to a_{13} ↓ a_{23} ↓ a_{33} ↓ a_{43} \to \to \to \to a_{14} ↓ a_{24} ↓ a_{34} ↓ a_{44}

- a_{ij} denotes the element in the i -th row and j -th column.

- a_{ii} represents the diagonal elements of the matrix.

D = d_{1} 0 ⋮ 0 0 d_{2} ⋮ 0 \dots \dots ⋱ \dots 00 ⋮ d_{n}

A = [a c b d] \Rightarrow A^{T} = [a b c d]

A square matrix where all elements are 0, except for 1s on the main diagonal (from top left to bottom right).
When any square matrix A is multiplied by the identity matrix I, the result is the original matrix A itself.

I_{n} = 10 ⋮ 0 02 ⋮ 0 \dots \dots ⋱ \dots 00 ⋮ 1

Identity Matrix: Properties: I, where I_{ij} = {10 if i = j, otherwise. For any square matrix A, A I = I A = A .

n [a d b e c f] = [na n d nb n e n c n f]

2 [1432] = [2 \cdot 1 2 \cdot 4 2 \cdot 3 2 \cdot 2] = [2864]

a c e b d f + g i k h j l = a + g c + i e + k b + h d + j f + l

[1432] + [5678] = [1 + 5 4 + 6 3 + 7 2 + 8] = [6101010]

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