Algebra - vocabulary

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M

Matrix

Matrix, n.

Pronounciation:

Brit. /ˈmeɪtrɪks/

Plural:

matrices, Brit. /ˈmeɪtrᵻsiːz/

Meaning:

A supporting or enclosing structure.

Source:

OED

Minor

Noun

Pronunciation
/'mʌɪnə/ listen

Meaning
Minor of a matrixA is the determinant of a smaller square matrix. Minor M_ij is obtained from matrix A by removing the i-th row and the j-th column.

Example
Minor of the matrix

can be computed as

Synonym
Subdeterminant

Related terms
Minor expansion of a determinant

Etymology
Anglo-Norman and Old French, Middle French menor, menour, menur smaller, lesser, younger (c1100; also used as noun in plural denoting people under the age of majority (13th cent.))

Source
OED

Monomial

Noun, adjective
Prefix: mono-
Suffix: -al

Pronunciation
/mɒˈnəʊmɪəl/ listen

Meaning
A monomial is a polynomial which has only one term.

Example
5x³

Antonym
Polynomial

Etymology
The prefix mono- means single + -nomial (in binomial n.); after French monôme monome n. (1691)

Source
OED

Moore-Penrose inverse

For A∈ℂ^(n x m), the Moore-Penrose inverse A^(+)∈ℂ^(m x n) is a matrix, satisfying all of the following conditions:

${\text{1.}}\quad AA^{+}A$ $=\;A$

${\text{2.}}\quad A^{+}AA^{+}$ $=\;A^{+}$

${\text{3.}}\quad (AA^{+})^{*}$ $=\;AA^{+}$

${\text{4.}}\quad (A^{+}A)^{*}$ $=\;A^{+}A$

The Moore-Penrose inverse exists for any A and is unique.

source