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Linear Algebra - Matrix Transformations
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Determinant
A scalar value that is a function of a square matrix representing the volumetric scaling factor when the matrix is viewed as a transformation.
Transpose Matrix
A matrix obtained by switching the rows and columns of the original matrix.
Symmetric Matrix
A matrix that is equal to its transpose.
Identity Matrix
A matrix that leaves the object unchanged when applied.
Translation Matrix
A non-linear transformation matrix that moves every point by a fixed distance in a given direction.
Trace of a Matrix
The sum of elements on the main diagonal of a square matrix.
Orthonormal Matrix
A square matrix with columns and rows that are orthonormal vectors.
Singular Matrix
A matrix that does not have an inverse.
Block Matrix
A matrix that is partitioned into several smaller matrices or blocks.
Reflection Matrix
A matrix that mirrors points across a specified axis.
Diagonal Matrix
A matrix where all off-diagonal elements are zero.
Eigenvalue and Eigenvector
A scalar and a non-zero vector associated with a matrix such that when the matrix is multiplied by the vector, the result is a scalar multiple of that vector.
Rotation Matrix
A matrix that rotates points in the plane around the origin.
Shear Matrix
A matrix that distorts the shape of an object such that its top and bottom faces slide over one another.
Rank of a Matrix
The maximum number of linearly independent column vectors in a matrix.
Orthogonal Matrix
A square matrix whose columns and rows are orthogonal unit vectors.
Invertible Matrix
A matrix that has an inverse, such that when multiplied by its inverse, it results in the identity matrix.
Projection Matrix
A matrix that projects a space onto a subspace, typically used to represent shadows or render 3D graphics on 2D screens.
Scaling Matrix
A matrix that enlarges or diminishes objects, scaling them by a factor.
Permutation Matrix
A matrix that changes the order of elements within a vector or matrix rows/columns.
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