Foundation of Matrix
# Matrix
A matrix is an array of numbers. This below is a 3x2 matrix.
notes
A vector is a n*1 matrix.
# Adding
::: notes note
The two matrices must be the same size
:::
# Multiplying
# To multiplying a single number
# To multiplying another matrix (dot product)
# Identity Matrix
Identity matrix is always "Square". It has 1s on the main diagonal and 0s everywhere else. Its symbol is the capital letter .
Example: 3x3 identity matrix.
For matrix and Identity matrix .
Note
For matrix and .
# Inverse of a Matrix
Just like a number has a reciprocal.
We write instead of because we don't divide by a matrix! The inverse of is only when:
# Orthogonal Matrix
Orthogonal Matrix is a real square matrix (opens new window) whose columns and rows are orthonormal (opens new window) vectors (opens new window). One way to express this is:
# Transposing
To "transpose" a matrix, swap the rows and columns.
We put a "T" in the top right-hand corner to mean transpose:
# References
Matrix Multiplying (opens new window)