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[[Image:lighterstill.jpg]][[Image:Mat9.jpg|right|frame]]

[[Image:lighterstill.jpg]][[Image:Mat9.jpg|right|frame]]

In [[biology]], '''matrix''' (plural: matrices) is the material (or tissue) in [[animal]] or [[plant]] [[cells]], in which more specialized [[structures]] are embedded, and a specific part of the [http://en.wikipedia.org/wiki/Mitochondrion mitochondrion] that is the site of oxidation of organic [[molecules]]. The internal structure of [http://en.wikipedia.org/wiki/Connective_tissue connective tissues] is an [http://en.wikipedia.org/wiki/Extracellular_matrix extracellular matrix]. Finger nails and toenails grow from matrices.

In [[biology]], '''matrix''' (plural: matrices) is the material (or tissue) in [[animal]] or [[plant]] [[cells]], in which more specialized [[structures]] are embedded, and a specific part of the [https://en.wikipedia.org/wiki/Mitochondrion mitochondrion] that is the site of oxidation of organic [[molecules]]. The internal structure of [https://en.wikipedia.org/wiki/Connective_tissue connective tissues] is an [https://en.wikipedia.org/wiki/Extracellular_matrix extracellular matrix]. Finger nails and toenails grow from matrices.

In [[mathematics]], a '''matrix''' (plural matrices, or less commonly matrixes) is a rectangular array of [[number]]s. This way, matrices can record other data that depend on multiple parameters. In particular they are used to keep track of the coefficients of multiple linear equations. Matrices are closely connected to linear transformations, which are higher-dimensional analogs of linear functions, i.e., functions of the form ''f''(''x'') = ''c'' · ''x'', where ''c'' is a constant. This map corresponds to a matrix with one row and column, with entry ''c''. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication, which displays a number of features not encountered in numbers; for example, products of matrices depend on the order of the factors, unlike products of [[real number]]s, say, where [[commutativity|''c - d'' = ''d - c'' for any two numbers ''c'' and ''d''.

In [[mathematics]], a '''matrix''' (plural matrices, or less commonly matrixes) is a rectangular array of [[number]]s. This way, matrices can record other data that depend on multiple parameters. In particular they are used to keep track of the coefficients of multiple linear equations. Matrices are closely connected to linear transformations, which are higher-dimensional analogs of linear functions, i.e., functions of the form ''f''(''x'') = ''c'' · ''x'', where ''c'' is a constant. This map corresponds to a matrix with one row and column, with entry ''c''. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication, which displays a number of features not encountered in numbers; for example, products of matrices depend on the order of the factors, unlike products of [[real number]]s, say, where [[commutativity|''c - d'' = ''d - c'' for any two numbers ''c'' and ''d''.

There are a number of operations that can be applied to modify matrices called ''matrix addition'', ''scalar multiplication'' and ''transposition'' These form the basic techniques to deal with matrices.

There are a number of operations that can be applied to modify matrices called ''matrix addition'', ''scalar multiplication'' and ''transposition'' These form the basic techniques to deal with matrices.

[[Image:Table2bigger.jpg]]

[[Image:Table2bigger.jpg]]

Familiar properties of numbers extend to these operations of matrices: for example, addition is [[commutative]], i.e. the matrix sum does not depend on the order of the summands: '''A''' + '''B''' = '''B''' + '''A'''.  The transpose is compatible with addition and scalar multiplication, as expressed by (''c'''''A''')^''T'' = ''c''('''A'''^''T'') and ('''A''' + '''B''')^''T'' = '''A'''^''T'' + '''B'''^''T''. Finally, ('''A'''^''T'')^''T'' = '''A'''.[http://en.wikipedia.org/wiki/Matrix_(mathematics)]

Familiar properties of numbers extend to these operations of matrices: for example, addition is [[commutative]], i.e. the matrix sum does not depend on the order of the summands: '''A''' + '''B''' = '''B''' + '''A'''.  The transpose is compatible with addition and scalar multiplication, as expressed by (''c'''''A''')^''T'' = ''c''('''A'''^''T'') and ('''A''' + '''B''')^''T'' = '''A'''^''T'' + '''B'''^''T''. Finally, ('''A'''^''T'')^''T'' = '''A'''.[https://en.wikipedia.org/wiki/Matrix_(mathematics)]

==All Definitions==

==All Definitions==

*'''I. A supporting or enclosing structure'''.

*'''I. A supporting or enclosing structure'''.