How-To: Comparison Operators

https://ss64.com/ps/syntax-compare.html

The following operators are all Case-Insensitive by default:

 -eq             Equal
 -ne             Not equal
 -ge             Greater than or equal
 -gt             Greater than
 -lt             Less than
 -le             Less than or equal
 -like           Wildcard comparison
 -notlike        Wildcard comparison
 -match          Regular expression comparison
 -notmatch       Regular expression comparison
 -replace        Replace operator
 -contains       Containment operator
 -notcontains    Containment operator
 -in             Like –contains, but with the operands reversed.(PowerShell 3.0)
 -notin          Like –notcontains, but with the operands reversed.(PowerShell 3.0)

To perform a Case-Sensitive comparison just prefix any of the above with "c"
for example -ceq for case-sensitive Equals or -creplace for case-sensitive replace.

Similarly prefixing with "i" will explicitly make the operator case insensitive.

Types
 -is     Is of a type
 -isnot  Is not of a type
 -as     As a type, no error if conversion fails

Logical operators
 -and    Logical And
 -or     Logical Or
 -xor    Logical exclusive Or
 -not    logical not
  !      logical not

Bitwise operators 
 -band   Bitwise and
 -bor    Bitwise or
 -bXor   Bitwise OR (exclusive)
 -bNot   Bitwise NOT
 -shl    Shift bits left (PowerShell 3.0)
 -shr    Shift bits right – preserves sign for signed values.(PowerShell 3.0)
 
Format Operator
 "format_string" -f Object1, Object2,...

The format_string is in the form: {0,-5} {1,-20} {2,-10}
In each set of braces, the first number, before the comma refers to the column.
The second number, after the comma determines the padding (how many characters)
If the second number is negative, it not only pads the element, but aligns it vertically. Optionally the second number can be used for formatting :hh :mm :C :p

When applied to an array, comparison operators will work as a filter returning all the values which match.

Filters

A PowerShell Filter will accept the following operators
-eq
-ne
-ge
-gt
-lt
-le
-like
-notlike
-approx
-bor
-band
-recursivematch

Notice that this list misses out several useful operators such as -match and -contains but those can still be used by piping to a Where-Object clause:
... | Where {$_.name –match 'value'}

Examples

$demo = $null
if (-Not ($demo)) { write "Zero, null or Empty"}
if (!($demo)) { write "Zero, null or Empty"}

$myVar -is "String"
$myVar -eq 123
$myVar -ceq $myVar2
"abcdef" -like "abc*"
"abcdef" -replace "dEf","xyz"
$myVar1 -is "String" -and $myVar2 -is "Int"
"{2:N}" -f 24.4567(1 -eq 1) -and -not (2 -gt 2)

$mycmd = ps | select id,ProcessName
foreach ($proc in $mycmd) {"{0,-8}{1,-20}" -f $proc.id, $proc.ProcessName}