Zero Matrix
To initialize some algorithm, sometimes you need to prepare a matrix of a known size containing all zero elements. Such matrix that all its elements equal to zero is called matrix zero, or null matrix .
Null matrix is fully determined by its size.
Example:
This simple interactive program below will produce null matrix at different size. This program is designed to confirm your basic understanding about zero matrix or null matrix.
Properties
Some well known properties of null matrix are
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Multiplication
of any matrix with null matrix will produce null matrix,
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Addition
of any matrix with null matrix (of the same size) produces the matrix itself, thus zero matrix serves as an
additive identity
,
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Subtraction
of a matrix from a null matrix produces the negative of that matrix,
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Subtraction of a matrix by a null matrix produces the matrix itself,
See also : matrix addition , matrix subtraction
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