MATRIX

1 / 23

# MATRIX - PowerPoint PPT Presentation

MATRIX. CONCEPT OF MATRIX. 1.Definition of matrix Equations. Rectangular number table can be formed from the coefficients. This is a matrix. The rectangular number table with m rows and n columns constructed by m n numbers in a certain order is called a m n

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'MATRIX' - laszlo

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
CONCEPT OF MATRIX
• 1.Definition of matrix Equations

Rectangular number table can be formed

from the coefficients

This is a matrix

The rectangular number table

with m rows and n columns

constructed by mn numbers in

a certain order is called a mn

Matrix (briefly matrix).

The horizontals are called the rows of matrix and

the verticals are called the columns of matrix

Is called the element located row i and column j.

The matrix is called real matrix if

its elements are real numbers.From now on,

we only discuss the real matrix.

Matrix is usually denoted with capital A、B、

C and so on. For instance

Simply write:

Column

matrix

Footmark

Row matrix

The main

diagonal line

The matrix is called a square

matrix if its row number

is equal to its column number,

i.e., m=n.

6.Trapezoid matrix Let

If

holds for i>j (i<j), and the number of zero before (behind)

the first (last) nonzero element is growing larger (less) as

the rows increase, then we call A a upper (lower)

trapezoid matrix.

They are all called trapezoid matrixes.

???

No!

Are they Trapezoid matrixes?

Trapezoid matrix is the most frequently-used matrix.

Operation of matrix

1.Equality: equality of two matrixes means that

their number of rows and number of columns

are respectively equal and their corresponding

elements are the same. i.e.,

=

corresponding

elements are the same

same type

Type is the same

define

Let

and

Obviously, A+B=B+A (A+B)+C=A+(B+C)

A+O=O+A=A A-A=O

Negative matrix: the negative matrix of

is

We write-A, i.e.,

3.number multiple

Is called the product of number and matrix，

Briefly number multiple。write：kA

=

In general，we have

what condition can enable A and B to multiply?

= O

Obviously

It is the difference

between Matrix and

number.

Example2

But

1.The multiplication of matrixes

does not satisfy commutative law;

2. does not satisfy cancellation law；

3. Has nonzero zero factor.

This is another

difference between

matrix

and number.

notice property 5.

The conclusion does

not hold if the orders of

A and B are not equal.

Positive integer power of the square matrix.

Transposition of matrix.

=

=

That is

Symmetric and anti-symmetric matrix

Any square matrix can be decomposed

to the sum of a symmetric matrix

and an anti-symmetric matrix.

The determinant of an odd

order anti-symmetric matrix

equals to zero.

0