Introduction
Matrices are fundamental objects in
linear algebra. But after all — what is a matrix?
What is a matrix?
A matrix is a rectangular array of
numbers arranged in rows and columns. If the matrix has m rows and n columns,
we say it is a matrix of order m × n (read: 'm by n'). Matrices are usually
denoted by uppercase bold letters, like A, B, or M.
General form
A general matrix looks like this:
Examples of matrices
1. A 4×4 matrix:
2. A 2 x3 matrix:
When are matrices useful?
Matrices are essential for:
🔹 Solving systems of linear equations
🔹 Representing data in statistics and machine learning
🔹Describing transformations in geometry
🔹Working with equations in economics, physics, and engineering
Common types of matrices
🔺 Square matrix: a matrix with the same
number of rows and columns (n × n).
🔺Row matrix: a matrix with only one
row (1 × n).
🔺 Column matrix: a matrix with only one column (m × 1).
🔺Zero matrix: a matrix in which all elements are zero.
🔺Identity matrix: a square matrix with
1’s on the main diagonal and 0’s elsewhere.
🔺 Diagonal matrix: a square matrix where all non-diagonal elements are zero.
🔺Symmetric matrix: a square matrix that is equal to its transpose.
🔺 Transpose of a matrix: a matrix
obtained by switching rows and columns.
Conclusion
A matrix is more than just a table of
numbers — it's a structured tool that helps organize and operate on data
efficiently. Now that you know what a matrix is, you're ready to explore
operations involving matrices and their properties.
📘
Next post: Matrix operations — how to add, subtract, and multiply matrices.
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