Math 2.0

Linear and multilinear algebra; matrix theory Proposition

Determinant of the identity matrix

Builds on DeterminantIdentity matrix

Statement

Let KK be a commutative ring and let n≥1n \ge 1. Then det⁡In=1\det I_n = 1, where InI_n is the identity matrix and det⁡\det is the determinant.

Remarks

This is property 3 of the definition of the determinant. It fixes the scale: the unit cube has volume 11. More generally, the determinant of a diagonal matrix is the product of its diagonal entries.

Reading path

To understand this page from the ground up, read these 9 pages in order. The foundations come first.

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Identity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionVector space, definition, no evidence levelVector spacedefinitionSquare matrix, definition, no evidence levelSquare matrixdefinitionLinear map, definition, no evidence levelLinear mapdefinitionMultilinear map, definition, no evidence levelMultilinear mapdefinitionAlternating multilinear map, definition, no evidence levelAlternating multiline…definitionDeterminant, definition, no evidence levelDeterminantdefinitionDeterminant of the identity matrix, statement, no evidence levelDeterminant of the id…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Identity matrix object
  2. Matrix definition
  3. Vector space definition
  4. Square matrix definition
  5. Linear map definition
  6. Multilinear map definition
  7. Alternating multilinear map definition
  8. Determinant definition
  9. Determinant of the identity matrix statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Determinant, Basic rules
About this page
Tag0Z4BWARC38
URIm2://0Z4BWARC38
Kindstatement, proposition
WritingW0 stub
MSC15A15
StatusThis copy of the site has no build data. Run m2 status 0Z4BWARC38.
UsesDeterminant, Identity matrix

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