# Linear Algebra Symbols

Linear Algebra: Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.

Symbol Symbol Name Meaning / definition Example
dot scalar product  b
× cross vector product × b
AB tensor product tensor product of A and B A  B inner product
[ ] brackets matrix of numbers
( ) parentheses matrix of numbers
A | determinant determinant of matrix A
det(A) determinant determinant of matrix A
|| x || double vertical bars norm
A T transpose matrix transpose (AT)ij = (A)ji
A  Hermitian matrix matrix conjugate transpose (A)ij = (A)ji
A * Hermitian matrix matrix conjugate transpose (A*)ij = (A)ji
A -1 inverse matrix A A-1 = I
rank(A) matrix rank rank of matrix A rank(A) = 3
dim(U) dimension dimension of matrix A rank(U) = 3
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