projection matrix
A 'projection matrix' is a fundamental concept in linear algebra and statistics, used to map vectors onto subspaces.
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Definition
C1Linear Algebra
(technical, academic)A square matrix that maps vectors onto a subspace, satisfying the condition that applying the matrix twice is the same as applying it once.
Example
- In linear algebra, a projection matrix is used to project vectors onto a subspace.
- The projection matrix ensures that any vector projected onto the subspace remains unchanged if projected again.
C1Statistics
(technical, academic)A matrix that transforms a vector of observed values into a vector of predicted values.
Example
- In regression analysis, the projection matrix maps observed data to fitted values.
- The projection matrix is crucial for calculating residuals in statistical models.
Similar
Terms that have similar or relatively close meanings to "projection matrix":
matrix algebraback projectionmatrix diagramfirst angle projection