Special Matrices & Vectors
Diagonal Matrix
For such matrices, only diagonal entries are non-zero.
Symmetric Matrix
Symmetric matrices are equal to their transpose.
Unit Vector
Vector with unit "length".
For example, both and are unit vectors.
Unit Basis Vector
An important set of vectors is the set of unit basis vectors given by:
Here, the “1” appears as the component indexed by j. Thus, we get the set given by:
These vectors are also referred to as the standard basis vectors.
Orthogonal Vectors
Two vectors are called orthogonal to each other if they are mutually prependicual vectors.
Also, orthonormal vectors are unit vectors prependicular to each other.
Orthogonal Matrix
A matrix is orthogonal if its transpose is equal to its inverse.
Identity matrix is a orthogonal matrix. Also, all columns are orthonormal.
Further, orthogonal matrices represent rotational operations which preserve volume.
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