What is Linear Algebra Symbols?
Linear algebra is a branch of mathematics that deals with linear equations, vectors, matrices, and their properties. It uses various symbols to represent mathematical concepts and operations. Here are some commonly used symbols in linear algebra:
- Scalars: Scalars are single numbers, and they are represented by lowercase letters such as a, b, c, etc.
- Vectors: Vectors are represented by boldface lowercase letters such as $\textbf{v}$, $\textbf{w}$, $\textbf{u}$, etc.
- Matrices: Matrices are represented by uppercase letters such as A, B, C, etc.
- Transpose: The transpose of a matrix is represented by a superscript “T” such as $A^T$.
- Dot product: The dot product of two vectors $\textbf{v}$ and $\textbf{w}$ is represented by $\textbf{v} \cdot \textbf{w}$.
- Cross product: The cross product of two vectors $\textbf{v}$ and $\textbf{w}$ is represented by $\textbf{v} \times \textbf{w}$.
- Identity matrix: The identity matrix is represented by I.
- Inverse: The inverse of a matrix is represented by $A^{-1}$.
- Determinant: The determinant of a matrix A is represented by $|A|$.
- Eigenvalues: Eigenvalues of a matrix A are represented by $\lambda_1, \lambda_2, \ldots, \lambda_n$.
- Eigenvectors: Eigenvectors of a matrix A are represented by $\textbf{x}_1, \textbf{x}_2, \ldots, \textbf{x}_n$.
- Null space: The null space of a matrix A is represented by Null(A).
- Column space: The column space of a matrix A is represented by Col(A).
- Rank: The rank of a matrix A is represented by rank(A).
LINEAR ALGEBRA SYMBOLS
Here are the list of Linear Algebra symbols with their names and meanings.
| Symbol | Symbol Name | Meaning |
| × | cross | vector product |
| · | dot | scalar product |
| A⊗B | tensor product | tensor product of A and B |
| 〈x , y〉 | inner product | |
| [ ] | brackets | matrix of numbers |
| ( ) | parentheses | matrix of numbers |
| | A | | determinant | determinant of matrix A |
| det(A) | determinant | determinant of matrix A |
| A-1 | inverse matrix | A A-1 = I |
| A T | transpose | matrix transpose |
| A* | Hermitian matrix | matrix conjugate transpose |
| A† | Hermitian matrix | matrix conjugate transpose |
| || x || | double vertical bars | norm |
| dim(U) | dimension | dimension of matrix A |
| rank(A) | matrix rank | rank of matrix A |
