definition of \((j, l)\)-minor of matrix
Topics
About: matrices space
The table of contents of this article
Starting Context
- The reader knows a definition of %ring name% matrices space.
Target Context
- The reader will have a definition of \((j, l)\)-minor of matrix.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( R\): \(\in \{\text{ the rings }\}\)
\( m\): \(\in \mathbb{N} \setminus \{0, 1\}\)
\( n\): \(\in \mathbb{N} \setminus \{0, 1\}\)
\( M\): \(\in \{\text{ the } m \times n R \text{ matrices }\}\)
\( j\): \(\in \{1, ..., m\}\)
\( l\): \(\in \{1, ..., n\}\)
\(*M^{j, l}\): \(= \text{ the matrix made by removing the }j \text{ -th row and the } l \text{ -th column of } M\), \(\in \{\text{ the } (m - 1) \times (n - 1) R \text{ matrices }\}\)
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Conditions:
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2: Note
We denote any element of \(M\) always like \(M^j_l\), because \(M^{j, l}\) and \(M_{j, l}\) will be understood as the \((j, l)\)-minor and the \((j, l)\)-cofactor.
The notation, \(M^{j, l}\), is not particularly prevalent in the literature (there does not seem to be any prevalent notation).
