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Matrix - Coggle Diagram
Matrix
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Rank of a matrix
Full rank matrix
A matrix is of full rank if its rank is equal to the smallest of the number of its rows or columns.
A full-rank square matrix is invertible.
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The maximum number of linearly independent row or column vectors in the matrix.Importance:
- Determines the dimension of the column space.
- Related to the solutions of linear equations.
Trace of a matrix
The sum of the elements on the main diagonal of a square matrix.Properties:
- Invariant under matrix similarity.
- Used in various matrix theorems.
Inverse of a matrix
A matrix that, when multiplied by the original matrix, yields the identity matrix.
Conditions:
- Only square matrices have inverses.
- A matrix has an inverse if and only if it is of full rank.