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Matrices

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. Matrices are fundamental in linear algebra and have applications in various fields such as physics, engineering, computer science, and economics. They are typically denoted by uppercase letters, such as A, B, or C.

Matrices can be classified based on their dimensions. A matrix with m rows and n columns is

Matrices can be added, subtracted, and multiplied. Addition and subtraction are performed element-wise, provided that the

Matrices can also be multiplied by scalars, which involves multiplying each element of the matrix by the

In addition to arithmetic operations, matrices can be transposed, which involves flipping the matrix over its

Matrices are used to represent linear transformations, solve systems of linear equations, and perform various computations

called
an
m-by-n
matrix.
For
example,
a
2-by-3
matrix
has
two
rows
and
three
columns.
Special
cases
include
square
matrices,
where
the
number
of
rows
equals
the
number
of
columns
(m
=
n),
and
vectors,
which
are
matrices
with
only
one
row
or
one
column.
matrices
have
the
same
dimensions.
Matrix
multiplication
is
more
complex
and
involves
a
dot
product
of
rows
and
columns.
The
product
of
an
m-by-n
matrix
and
an
n-by-p
matrix
is
an
m-by-p
matrix.
scalar.
This
operation
is
known
as
scalar
multiplication.
diagonal,
swapping
rows
with
columns.
The
transpose
of
a
matrix
A
is
denoted
by
A^T.
in
computer
graphics
and
machine
learning.
They
are
a
powerful
tool
for
organizing
and
manipulating
data
in
a
structured
and
efficient
manner.