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[edit] Glossary of matrix theory

The terms below are used in the branch of mathematics called matrix theory, which is often considered a subfield of linear algebra. For specific types of matrices, see the List of matrices. For some matrix operations, see Matrix.

Matrix
A rectangular array of objects which are usually members of a ring.
The definitions below will assume the following matrix:
A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} = (a_{ij})_{i=1,\ldots,m \atop j=1,\ldots,n}
Element
One of the objects in a matrix.
aij for a specific choice of i and j.
Size or dimensions
The number of rows and columns, respectively, of a matrix; usually expressed in the form m × n, read "m by n".
i-th row of matrix A
\begin{bmatrix} a_{i1} & a_{i2} & \cdots & a_{in} \end{bmatrix}
j-th column of matrix A
\begin{bmatrix} a_{1j} \\ a_{2j} \\ \vdots \\ a_{mj} \end{bmatrix}
Main diagonal
The elements whose row and column number match.
\{a_{kk}:\,k = 1, \ldots, \min(m,n)\}
Transpose
An operation resulting in a new matrix whose rows are the columns of the original matrix and whose columns are the rows of the original matrix, or the resulting matrix itself.
A^T = (a_{ji})_{i=1,\ldots,m \atop j=1,\ldots,n}
Trace
The sum of the elements on the main diagonal.
\mbox{tr}\,A = a_{11} + a_{22} + \ldots + a_{kk}, \mbox{ where } k=\min(m,n)

...

Minor
The determinant of the matrix obtained by deleting a given row and column from the original matrix.
M_{ij}=\begin{vmatrix} a_{11} & \cdots & a_{1,j-1} & a_{1,j+1} & \cdots & a_{1n} \\ \vdots & & \vdots & \vdots & & \vdots \\ a_{i-1,1} & \cdots & a_{i-1,j-1} & a_{i-1,j+1} & \cdots & a_{i-1,n} \\ a_{i+1,1} & \cdots & a_{i+1,j-1} & a_{i+1,j+1} & \cdots & a_{i+1,n} \\ \vdots & & \vdots & \vdots & & \vdots \\ a_{m1} & \cdots & a_{m,j-1} & a_{m,j+1} & \cdots & a_{mn} \end{vmatrix}
Note that the i-th row and j-th column are missing in the above determinant.

...

Vector
A matrix with one row (a row vector) or one column (column vector).
See Vector for more information.
Linear transformation
The function that results from multiplying a given matrix by an appropriately sized vector of variables.
f:\mathbb{R}^n\to\mathbb{R}^m,\mbox{ where }f(x)=Ax,\ x\in\mathbb{R}^n.
Rank
The dimension of the space generated by the rows of a given matrix.
The dimension of the image of the linear transformation represented by the matrix.

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'''dcljr''' is a [[:en:Mathematics|math]] [[:en:Tutor|tutor]] ([[tutor]]) who lives in
[[:en:Austin, Texas|Austin, Texas]] ([[Austin, Texas]]; [[Austin]], [[Texas]]).

Sorry, I don't speak [[:en:FOO language|FOO]].
My native language is [[:en:English language|English]].
([[:en:User:Dcljr]])
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[edit] List of CPU flags

others: acpi/ACPI, clflush/CLFLUSH, dts/DTS, ht/HT, mce/MCE, ss/SS, sse2/SSE2, sse3/SSE3, tm/TM

what about: AVR instruction set?, Register Transfer Language?