Linear Algebra Symbols (original) (raw)
Last Updated : 27 Feb, 2026
Linear Algebra Symbols are mainly focused on comprehending how various systems of linear equations behave and may be solved. This is performed by storing the equations in matrices and vectors, both of which are mathematical objects that may be handled in several ways.
Table of Linear Algebra Symbols
Linear algebra includes the study of matrices, set theory, determinants, etc. The below table shows the linear algebra symbols and their names, meanings, and examples for each.
| SYMBOL | NAME | EXAMPLE | ||
|---|---|---|---|---|
| . | dot | a.b | ||
| x | cross | a x b | ||
| A B | tensor product | A B | ||
| [ ] | Square Brackets | x has a place with the closed interval from 3 to 7, including the both endpoints. This is indicated x as ∈ [3,7]. | ||
| { } | Curly Brackets or Set Symbol | 5 × { 4 + 5 }Here, the curly brackets indicates that the addition operation inside should be perform before multiply with 5If set A is a set of first 3 natural numbers, then A = {1, 2, 3 } | ||
| ( ) | Parentheses | (4 + 4) × 3Here, parentheses indicate that addition operation should be perform before multiplying. | ||
| {A} | Set A | If set A is set of even numbers then{A} = {2, 4, 6, 8…} | ||
| ⊆ | Subset | A = {1, 3, a}B = {a, b, 1, 2, 3, 4, 5}A ⊆ B | ||
| ⊂ | Proper Subset | A = {1, 2, a}B = {a, b, c, 2, 4, 5, 1} A ⊂ B | ||
| ⊄ | Not a Subset | A = {1, 2, 3}B = {a, b, c}A ⊄ B | ||
| ⊇ | Superset | Integeer is superset of Natural Number | ||
| Ø | Empty Set | { } = Ø | ||
| P(X) | Power Set | If A = {a, b}P(A) = {{ }, {a}, {b}, {a, b}} | ||
| ⋃ | Union of Set | A = {2, 3, 4}, B = {2, 4, 6}Then A ⋃ B = {2, 3, 4, 6} | ||
| ⋂ | Intersection of Set | A = {2, 3, 4}, B = {2, 4, 6}Then A ⋂ B = {2, 4} | ||
| n(A) | Cardinality of Set | A = {2, 4, 6} then n(A) = 3 | ||
| Φ | Null Set | Set of Natural Number greater than 2 but less than 3 | ||
| ℕ | Set of natural numbers | 0, 1, 2, 3, … | ||
| ℤ | Set of integers | -3, -2, -1, 0, 1, 2, 3, … | ||
| ℝ | Set of real numbers | π, e, √2, 3/2, … | ||
| Aij | Matrices | A3x2 = \begin{bmatrix} 1& 2\\3 & 4 \\ 5& 6\\ \end{bmatrix} | ||
| | A | or det(A) | Determinant | If we have matrix A = \begin{bmatrix} 1& 2\\ 3& 4\\ \end{bmatrix}then |A | = |
| AT | Tanspose of Matrix | If we have matrix A = \begin{bmatrix} 1& 2\\ 3& 4\\ \end{bmatrix} then AT =\begin{bmatrix} 1& 3\\ 2& 4\\ \end{bmatrix} | ||
| A-1 | Inverse of Matrix | For Matrix A = \begin{bmatrix} 1& 2\\ 3& 4\\ \end{bmatrix}A-1 = \begin{bmatrix} -2& 1\\ 3/2& -1/2\\ \end{bmatrix} | ||
| A* | Hermitian Matrix | For matrix A, A = AH where AH is the conjugate transpose of matrix A. (A*)ij =(AT)ji | ||
| rank(A) | matrix rank | rank(A) =3 | ||
| dim(U) | dimension | rank(U) =3 | ||
| + | addition | Solve 5 + 5solution = 10 | ||
| - | subtraction | Solve 7- 5solution = 2 | ||
| * or x | multiplication | Solve 5 x 5solution = 25 | ||
| / or ÷ | division | Solve 10 / 5solution = 2 | ||
| = | Equal to | 5 + 5 = 10 Here ,The equal sign denotes that the sum of 5 and 5 is equal to 10 | ||
| ≠ | Not equal to | 5 ≠ 3The not equal to sign indicates that 5 is not equal to 3 | ||
| < | Less than | 12 < 15Solution : True, Because 12 is less than of 15 | ||
| > | Greater than | 15 > 5Solution : True, Because 15 s greater than of 5 | ||
| ≤ | Less than or equal To | x ≤ 5Here x is less than or equal to 5 | ||
| ≥ | Greater than or Equal To | x ≥ 6Here x is greater than or equal to 6 | ||
| ≪ | Much less than | 1 ≪ 100It means 1 is much less than 100 | ||
| ≫ | Much greater than | 1 ≫ 100it means 1 is much greater than 100 | ||
| ⋉ | Directly Proportional | The total bill increases if you buy more product. Hence, total bill is directly proportional to number of objects | ||
| |x | modulus | It finds the modulus of x |
**Also check:
Linear Algebra Symbols Solved Examples
**Example 1: Find the sum of the two vectors \overrightarrow{\rm A}**= 3i + 4j + 5k and \overrightarrow{\rm B}**= -i + 2j + k.
**Solution:
\overrightarrow{\rm A} + \overrightarrow{\rm B}= (3-1)i + (4 + 2)j + (5 + 1)k = 2i + 6j + 6k
**Example 2: Find the sum of the two matrices
\begin{bmatrix} 3 & 3\\ 4 & 6\\ \end{bmatrix} and \begin{bmatrix} 1 &-2 \\ 3 & 4 \end{bmatrix}?
**Solution:
Let the two matrices be P = \begin{bmatrix} 3 & 3\\ 4 & 6\\ \end{bmatrix}
Q = \begin{bmatrix} 1 &-2 \\ 3 & 4 \end{bmatrix}
S = P + Q = \begin{bmatrix} 3 & 3\\ 4 & 6\\ \end{bmatrix} + \begin{bmatrix} 1 &-2 \\ 3 & 4 \end{bmatrix} = \begin{bmatrix} 4 & 1\\ 7& 10\\ \end{bmatrix}
**Example 3: For the equation 2x – 3 = 2, solve for x.
**Solution:
6x – 3 = 2
⇒ 6x = 2 + 3
⇒ 6x = 5
⇒ x = 5 / 6 = 0.83
**Example 4: Find the intersection of both A = {2, 3, 4} and B = {2, 4, 6, 9, 11}.
**Solution:
A = {2, 3, 4}, B = {2, 4, 6,9,11}
Then A ⋂ B = {2, 4}
**Example 5: Given two values A = 5 and B = 20, Find the product of A and B
**Solution:
Product of A and B = A × B = 5 × 20 = 100
**Example 6: If the set A={3,5,7,9}, then find n(A).
**Solution:
n(A) denotes the number of elements in a given set, A={3,5,7,9} then n(A) = 4
Linear Algebra Symbols Practice Questions
**Q1. Given two values, A = 5 and B = 20, find the division of A and B.
**Q2. Find the union of both A = {2, 3, 4, 5} and B = {2, 4, 6, 9, 11}, A ⋃ B?
**Q3. If the set A={3,5,7,9}, then find P(A).
**Q4. If the set A={3,5,7,9,13}, then find n(A).
**Q5. For the equation 6y – 5 = 20, solve for y.