Are linked genes the ones that are linked with genes on the same chromosome or with genes on the homologous chromosome?

Some genes are "linked" to each other because you inherit them together.
Inherit one, inherit the other.

You inherit them together because they are on the same chromosome, and when the gametes are formed by meiosis, they receive the entire chromosome from the original cell.

However, it turns out that when the chromosome pairs line up during meiosis, they often swap whole sections.

This swapping is called "crossing over," which disrupts the linkage between genes by "unlinking" them.

Here's an image showing crossing over

https://tutor.hix.ai

After a section of the chromosome crosses over to the homologous chromosome, the genes at the end are no longer linked with the genes on the rest of the chromosome.

Crossing over lets us map the location of genes on their chromosomes by finding the sequence of genes along the length of a chromosome.

The further apart the linked genes are on the chromosome, the more likely it is that a break will occur in between them.

But when two linked genes are close to each other, it is less likely that a random break will happen between them.

So by studying the frequency of crossing over between pairs of linked genes, scientists were able to determine if they were close or distant. The more common the crossing over, the more distant they are on the chromosome.

Here is an image of that idea

https://tutor.hix.ai

In any eukaryotic, diploid organism, each cell has 2n number of chromosomes i.e. chromosomes are represented in pairs. Homologous pair of chromosomes carry same genes, but there could be different alleles on a pair of homologues.

It is important to understand the relationship between linked genes, their alleles and crossing over between homologous chromosomes .

First thing first: linked genes are present on same chromosome, but corresponding alleles of these genes are present on homologous chromosome.**

Alleles present together on a chromosome tend to enter a gamete as a unit due to linkage.

Allelic recombination takes place through crossing over during meiosis: when two genes are closely located on a chromosome, there is less probability of crossing over-- hence linkage is strong.

Recombination between linked alleles takes place due to linkage and frequency of appearance of recombinants in a test cross help us to derive a linkage map. If there are 50% recombinants, there is no linkage.