今天给学生上课遇到一个很诡异的问题，学生们说根据定理，矩阵的秩为2，但是软件计算的秩是4或者3！！自己回来试，果然在MATLAB中的结果为3。想来不可能啊，{wy}的可能就是原来的分数在Matlab中都是近似为小数的（默认为4位），然后改数据表示格式：format long。果然如我所料，重新计算的秩为2。如释重负！

附format的相关语句：

format

Set display format for output
Graphical Interface

As an alternative to using the format command, you can also use the MATLAB Preferences GUI. Select File > Preferences > Command Window and press the Help button for more information.
Syntax

format
format type
format('type')

Description

Use the format function to control the output format of numeric values displayed in the Command Window.

Note   The format function affects only how numbers are displayed, not how MATLAB computes or saves them.

format by itself, changes the output format to the default appropriate for the class of the variable currently being used. For floating-point variables, for example, the default is format short (i.e., 5-digit scaled, fixed-point values).

format type changes the format to the specified type. The tables shown below list the allowable values for type.

format('type') is the function form of the syntax.

The tables below show the allowable values for type, and provides an example for each type using pi.

Use these format types to switch between different output display formats for floating-point variables.

Type

Result

short

Scaled fixed point format, with 4 digits after the decimal point. For example, 3.1416.

long

Scaled fixed point format with 14 to 15 digits after the decimal point for double; and 7 digits after the decimal point for single. For example, 3.141592653589793.

short e

Floating point format, with 4 digits after the decimal point. For example, 3.1416e+000.

long e

Floating point format, with 14 to 15 digits after the decimal point for double; and 7 digits after the decimal point for single. For example, 3.141592653589793e+000.

short g

Best of fixed or floating point, with 4 digits after the decimal point. For example, 3.1416.

long g

Best of fixed or floating point, with 14 to 15 digits after the decimal point for double; and 7 digits after the decimal point for single. For example, 3.14159265358979.

short eng

Engineering format that has 4 digits after the decimal point, and a power that is a multiple of three. For example, 3.1416e+000.

long eng

Engineering format that has exactly 16 significant digits and a power that is a multiple of three. For example, 3.14159265358979e+000.

Use these format types to switch between different output display formats for all numeric variables.

Value for type

Result

+

+, -, blank

bank

Fixed dollars and cents. For example, 3.14

hex

Hexadecimal (hexadecimal representation of a binary double-precision number). For example, 400921fb54442d18

rat

Ratio of small integers. For example, 355/113

Use these format types to affect the spacing in the display of all variables.

Value for type

Result

Example

compact

Suppresses excess line feeds to show more output in a single screen. Contrast with loose.theta = pi/2
theta =
  1.5708

loose

Adds linefeeds to make output more readable. Contrast with compact.theta = pi/2

theta =

  1.5708

Remarks

Computations on floating-point variables, namely single or double, are done in appropriate floating-point precision, no matter how those variables are displayed. Computations on integer variables are done natively in integer.

MATLAB always displays integer variables to the appropriate number of digits for the class. For example, MATLAB uses three digits to display numbers of type int8 (i.e., -128:127). Setting format to short or long does not affect the display of integer variables.

The specified format applies only to the current MATLAB session. To maintain a format across sessions, use MATLAB preferences. Specifying Options for MATLAB Using Preferences

To see which type is currently in use, type
get(0,'Format')

To see if compact or loose formatting is currently selected, type
get(0,'FormatSpacing').

Examples

Example 1

Change the format to long by typing
format long

View the result for the value of pi by typing
pi
ans =
   3.14159265358979

View the current format by typing
get(0,'format')
ans =
   long

Set the format to short e by typing
format short e

or use the function form of the syntax
format('short','e')

Example 2

When the format is set to short, both pi and single(pi) display as 5-digit values:
format short

pi
ans =
    3.1416

single(pi)
ans =
    3.1416

Now set format to long, and pi displays a 15-digit value while single(pi) display an 8-digit value:
format long

pi
ans =
    3.14159265358979

single(pi)
ans =
    3.1415927

Example 3

Set the format to its default, and display the maximum values for integers and real numbers in MATLAB:
format

intmax('uint64')
ans =
   18446744073709551615

realmax
ans =
  1.7977e+308

Now change the format to hexadecimal, and display these same values:
format hex

intmax('uint64')
ans =
   ffffffffffffffff

realmax
ans =
   7fefffffffffffff

The hexadecimal display corresponds to the internal representation of the value. It is not the same as the hexadecimal notation in the C programming language.
Example 4

This example illustrates the short eng and long eng formats. The value assigned to variable A increases by a multiple of 10 each time through the for loop.
A = 5.123456789;

for k=1:10
   disp(A)
   A = A * 10;
end

The values displayed for A are shown here. The power of 10 is always a multiple of 3. The value itself is expressed in 5 or more digits for the short eng format, and in exactly 15 digits for long eng:
  format short eng                format long eng

     5.1235e+000                5.12345678900000e+000
    51.2346e+000               51.2345678900000e+000
   512.3457e+000              512.345678900000e+000
     5.1235e+003                5.12345678900000e+003
    51.2346e+003               51.2345678900000e+003
   512.3457e+003              512.345678900000e+003
     5.1235e+006                5.12345678900000e+006
    51.2346e+006               51.2345678900000e+006
   512.3457e+006              512.345678900000e+006
     5.1235e+009                5.12345678900000e+009

Algorithms

If the largest element of a matrix is larger than 103 or smaller than 10-3, MATLAB applies a common scale factor for the short and long formats. The function format + displays +, -, and blank characters for positive, negative, and zero elements. format hex displays the hexadecimal representation of a binary double-precision number. format rat uses a continued fraction algorithm to approximate floating-point values by ratios of small integers. See rat.m for the complete code.