[Linear Algebra] 4. Matrix Types

1. Square Matrix

The square matrix is a type of matrix whose number of rows(noted as n) and columns(noted as m) are the same(n=m).

Figure 1. Example of the square matrix (3x3)

2. Symmetric Matrix

Symmetric matrix is a type of matrix where the elements in the top-right triangle of matrix are identical to its bottom-left triangle.

The axis of symmetry is the main diagonal of the matrix.

Figure 2. Example of the symmetric matrix

3. Triangular Matrix

[2] Triangular matrix is a type of square matrix that has all values in the upper-right or lower-left of the matrix with the remaining elements filled with zero values.

Figure 3. Example of the triangular matrix

4. Diagonal Matrix

Diagonal matrix is a type of matrix whose diagonal elements have non-zero values whereas all the other elements are zero.

In vector form, it is written as Diagonal matrix d = (d11, d22, d33)

Figure 4. Example of the diagonal matrix

5. Identity Matrix

Identity matrix is a type of matrix where only its diagonal elements have values of one and remaining elements are filled with zero. It is often notated as ‘I’, and called the ‘unit matrix’

The product of any square matrix and the appropriate identity matrix is always the original matrix,

Figure 5. The Identity Matrix 𝐈

[1] product = In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

6. Orthogonal Matrix

An orthogonal matrix is a type of square matrix whose columns and rows are orthogonal unit vectors.

Figure 6. The property of orthogonal matrix 𝑸

7. Codes with the library NumPy

8. Reference

[1]https://en.wikipedia.org/wiki/Product_(mathematics)

[2]https://machinelearningmastery.com/introduction-to-types-of-matrices-in-linear-algebra/

[3]https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/a/intro-to-identity-matrices

Any corrections, suggestions, and comments are welcome.