Linear Algebra, Notation
Up for GrabsUpdated 2 min read
Notation
ℝ, {ℝ}^{+}, {ℝ}^{n} | real numbers, reals greater than 0, ordered n-tuples of reals |
|---|---|
ℕ | natural numbers: \{ 0 , 1 , 2 , … \} |
ℂ | complex numbers |
\{ … \ | \ … \} | set of . . . such that . . . |
( a \ .. \ b ), [ a \ .. \ b ] | interval (open or closed) of reals between a and b |
⟨ … ⟩ | sequence; like a set but order matters |
V , W , U | vector spaces |
\overset{→}{v} , \overset{→}{w} | vectors |
\overset{→}{0}, {\overset{→}{0}}_{V} | zero vector, zero vector of V |
B , D | bases |
{ℰ}_{n} = ⟨ {\overset{→}{e}}_{1} , \ … , \ {\overset{→}{e}}_{n} ⟩ | standard basis for {ℝ}^{n} |
\overset{→}{β} , \overset{→}{δ} | basis vectors |
{R e p}_{B} ( \overset{→}{v} ) | matrix representing the vector |
{𝒫}_{n} | set of n-th degree polynomials |
{ℳ}_{n \ × \ m} | set of n \ × \ m matrices |
[ S ] | span of the set S |
M ⊕ N | direct sum of subspaces |
V ≅ W | isomorphic spaces |
h , g | homomorphisms, linear maps |
H , G | matrices |
t , s | transformations; maps from a space to itself |
T , S | square matrices |
{R e p}_{B , D} ( h ) | matrix representing the map h |
{h}_{i , j} | matrix entry from row i, column j |
| T | | determinant of the matrix T |
ℛ ( h ) , 𝒩 ( h ) | rangespace and nullspace of the map h |
{ℛ}_{∞} ( h ) , {𝒩}_{∞} ( h ) | generalized rangespace and nullspace |
Lower case Greek alphabet
\begin{matrix}\text{name} & \text{character} & \text{name} & \text{character} & \text{name} & \text{character} \\ \text{alpha} & α & \text{iota} & ι & \text{rho} & ρ \\ \text{beta} & β & \text{kappa} & κ & \text{sigma} & σ \\ \text{gamma} & γ & \text{lambda} & λ & \text{tau} & τ \\ \text{delta} & δ & \text{mu} & μ & \text{upsilon} & υ \\ \text{epsilon} & ϵ & \text{nu} & ν & \text{phi} & ϕ \\ \text{zeta} & ζ & \text{xi} & ξ & \text{chi} & χ \\ \text{eta} & η & \text{omicron} & o & \text{psi} & ψ \\ \text{theta} & θ & \text{pi} & π & \text{omega} & ω\end{matrix}
About the Cover.
This is Cramer's Rule for the system {x}_{1} + 2 {x}_{2} = 6, {}3 {x}_{1} + {x}_{2} = 8. The size of the first box is the determinant shown
(the absolute value of the size is the area). The size of the second box is {x}_{1} times that, and equals the size of the final box. Hence, {x}_{1} is the final determinant divided by the first determinant.
Where this page came from
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