[ Matrix ] 행렬 표기법 정리

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[ Matrix ] 행렬 표기법 정리

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Notation and Nomenclature

 

• $\mathbf{\text{A}}$ : 행렬 A → 행렬은 bold 대문자 표현 (중요)
• ${\mathbf{\text{A}}}^T$ : Transposed 행렬
• ${\mathbf{\text{A}}}^{-1}$ : 행렬 A 의 역행렬
• ${\mathbf{\text{A}}}^{-T}$ : Transposed 행렬의 역행렬 또는 반대 (${\mathbf{\text{A}}}^{-T}=({\mathbf{\text{A}}}^{-1}{)}^T=({\mathbf{\text{A}}}^T{)}^{-1}$)
• ${\mathbf{\text{A}}}^{+}$ : 행렬 A 의 Pseudo 역행렬 
• ${\mathbf{\text{A}}}^{\ast }$ : Complex conjugated 행렬
• ${\mathbf{\text{A}}}^H$ : Transposed & Complex conjugated 행렬 (Hermitian)
• ${\mathbf{\text{A}}}^{1/2}$ : 행렬의 Square root (unique 할떄), not elementwise
• $(\mathbf{\text{A}}{)}_{ij}$ = $A_{ij}$ : 행렬의 $(i,j)$ 번째 entry
• $[\mathbf{\text{A}}{]}_{ij}$ : $(i,j)$ - submatrix
• $\Vert \mathbf{\text{A}}\Vert$ : Matrix norm (subscript if any denotes what norm)

 

• $\text{det}(\mathbf{\text{A}})$ : Determinant of $\mathbf{\text{A}}$. (행렬식)
• $\text{Tr}(\mathbf{\text{A}})$ : Trace of the matrix $\mathbf{\text{A}}$. (행렬의 대각합)
• $\text{diag}(\mathbf{\text{A}})$ : 행렬 $\mathbf{\text{A}}$의 대각 행렬
• $\text{eig}(\mathbf{\text{A}})$ : Eigenvalues of the matrix $\mathbf{\text{A}}$. (고윳값)
• $\text{sup}$ : Supremum of a set. (집합의 상한)

 

• $A\circ B$ : Hadamard (elementwise) product.( latex : \circ )
• $A\otimes B$ : Kronecker product. ( latex : \otimes ) 

 

• $\mathbf{\text{0}}$ : The null matrix. 모든 요소가 영인 행렬
• $\mathbf{\text{I}}$ : The identity matrix. 
• ${\mathbf{\text{J}}}^{i,j}$ : The single-entry matrix. $(i,j)$ 에만 값이 존재하고 나머지는 모두 영인 행렬
• $\mathbf{\Sigma }$ : A positive definite matrix (Sigma)
• $\mathbf{\Lambda }$ : A diagonal matrix (Lambda)

 

• $\mathbf{\text{a}}$ : 벡터 (column-vector) $\mathbf{\text{a}}$ → 벡터는 bold 소문자 표현 (중요)
• $a_i$ : 벡터 $\mathbf{\text{a}}$ 의 $i$ 번째 요소 → 벡터의 요소는 소문자 표현 (중요)
• $a$ : 스칼라(scalar) → 스칼라는 소문자 표현 (중요)

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함께 읽어 볼 만한 글 

[ LaTeX ] 행렬 표현하기 (matrix, pmatrix, bmatrix, Bmatrix, vmatrix, Vmatrix)

[ LaTeX ] 행렬 표현하기 (matrix, pmatrix, bmatrix, Bmatrix, vmatrix, Vmatrix)

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[ 참고 ]

https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf

https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject

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