In other words, regardless of what Willy says or does, Linda is his constant support, and she never stops believing in him—she sees only the good. Linda tells Willy he is good-looking and loved by his sons. She says:

Willy, darling, you're the handsomest man in the world—

And...

Few men are idolized by their children the way you are.

Linda makes the things important in her husband's life, important to her. If he experiences self-doubt, she encourages him. In showing him how strong she believes in him, Linda wants Willy to also believe strongly in himself. These things show how much Linda loves her husband.

In Arthur Miller's play Death of a Salesman the character of Linda Loman is meant to represent a kind of foil, or opposite, of her husband, Willy.

While Willy is a man whose dreams dominate his actions, Linda is his anchor. The woman who remains in the same exact place expecting Willy, and accepting Willy for who he is. So much she supports Willy that she even goes out of her way to defend him:

LINDA: Then make Charley your father, Biff. You can’t do that, can you? I don’t say he’s a great man. Willy Loman never made a lot of money. His name was never in the paper. He’s not the finest character that ever lived. But he’s a human being, and a terrible thing is happening to him. So attention must be paid. He’s not to be allowed to fall into his grave like an old dog. Attention, attention must be finally paid to such a person....

Willy is also a man whose only quest is for the superficiality of things: Whatever looks good is good enough for him. One must be well-liked and attractive to "make it". Your children must be popular and overwhelming to be "it". Linda, however, remains in the back of the scene and simply witnesses everything, being the foundation upon which all the dysfunctional activity of the men of the family continues to fall.

This being said, it should suffice to say that, above everything, Linda is an extremely submissive person. She is submissive because she allows herself to have a very passive role in her own household. The men in her home, her sons and her husband, basically take the lead in everything that goes on. Willy pretty much takes it upon himself to instill a system of values, albeit bad ones, in his children while Linda, again, watches from the sidelines.

Even when Willy dies we see men surrounding Linda, her sons and Charley, while she remains oblivious as tho why nobody shows up at the funeral.

All of this demonstrates that Linda is a woman with very little initiative but with a huge amount of will and patience. Perhaps she is simply a symptom of her time:  An individual born and raised to be just that- a mother and a wife. Hence, with this role to fulfill Linda has unfortunately confused being a woman with being an object that is meant to spill out nurture and love. Linda is certainly quite used by her family: As a rock, and as a support system. Yet, Linda never gets her worth in appreciation, nor does she get much support in return. Linda is Willy's anchor until the end, and the shadow of her husband's overwhelming presence.

In Arthur Miller's Death of a Salesman, Linda is forever the peacekeeper, and supportive wife and mother. Unaware of her husband's affair (a fact that has driven a wedge between Biff—who discovered it—and Willy), Linda is always trying to protect her husband. Perhaps this is because she sees how beaten down he has become in not being more like his brother Ben, whose memory he not only idolizes, but whose presence he still imagines after Ben's death. To her, he must seem particularly fragile.

As Willie's "long-suffering" and "devoted" wife, Linda is symbolic of hope—believing that with enough of her love and vigilance, Willie can survive and make it through to another day. She protects Willie in this hope—taking her sons to task with regard to how they treat their father (ironically still not knowing the source of Biff's anger toward Willy—Willy's betrayal of her):

It sounds old-fashioned and silly, but I tell you he put his whole life into you and you've turned your backs on him...Biff, I swear to God! Biff, his life is in your hands.

Linda is also aware that Willy is suicidal. A witness to a car accident that Willy had said:

...he wasn't driving fast at all, and...he didn't skid. She says he came to that little bridge, and then deliberately smashed into the railing...

And...

...on the bottom of the water heater there's a new little nipple on the gas pipe...Every day I go down and take away that little rubber pipe. But, when he comes home, I put it back where it was...I live from day to day...

Linda is protective of all the men in her family, so it is no surprise that she acts this way with Willy and Biff. More than anything, she wants them all to be happy, even though none of them are realists; none has really had any success in life, but this does not dissuade her—she is a woman of undeniable inner-strength.

With all this, perhaps we can assume that Linda tells Biff to sleep because it is while he sleeps that he will not worry, and while he sleeps he need not fret about how fragile their family is. For Linda, her husband is her greatest love, even after so many years of marriage, and she does all she can—clinging to the hope that she can keep the family together, and keep Willy alive; however, she knows Biff cannot fix this problem either.

Kay Staton's 1991 essay, found in Willy Loman, asserts that Linda...

...is the support that enables [the Loman men] to continue despite their failures...

The quotation reflects a strong sense of this in Linda—her unwavering support, ceaseless love, and complete and unconditional acceptance.

Linda loves her husband and sons fiercely: more than she cares for herself.However, it is evident that Willy is the centre of her world.  She contributes to the failure of Willy by shoring him up and bolstering his confidence rather than gently pointing out reality. She tells Willy he is

 The handsomest man in the world

 And that he is

 idolized by his children

She is aware of his decline, but tries to support him in to believing other factors are responsible for his failure. She blames the car, his glasses and his overactive mind for his inability to drive properly. However, she does admit to Biff how worries she is for Willy-

 He’s not the finest character that ever lived. But he’s a human being, and a terrible thing is happening to him.

She is desperate to save him; telling Biff and Happy about his suicide plans as she is “ashamed” to challenge him about her discovery.

Willy does not treat Linda well. She makes do, as we see her darning her stockings, whilst he is seen giving stockings to the woman in his hotel room. When his is energised in seeing the potential in Biff, he cuts her out of the conversation

 WILLY [to LINDA] Will you stop!

Happy and Biff use their mother as much as Willy does. She is not invited to the meal at Frank’s Chop House. It is as if everyone expects her resilience to hold out.

It's not entirely clear that Linda Loman changes all that much. All throughout the play, she acts as Willy's enabler: protecting him, his fantasies, and his delusions from the harsh intrusion of reality. At no point does she ever confront Willy about his suicidal tendencies; she seems to think that the best way for Willy's mental health to improve is through his sons striving hard for success.

Her whole world revolves around Willy, and she puts her husband's needs ahead of her own and her sons' every single time. The quintessential 50s housewife, Linda is loyal, patient, and submissive to her husband. Only she acts more like a mother than a wife, and therein lies the problem. Willy doesn't need a mother, doesn't need to be coddled; he needs someone to shake some sense into him, to get him to see that his current path can only lead to destruction for himself and sadness for those left behind. Linda is not that someone. Her inability to change rubs off on her husband, with fatal consequences.

Linda's character definitely reads more like a devout wife than a sacrificed parent. If anything, she is more of a mother and caretaker to her own husband than she is to Biff and Happy. Linda has a mission in her life, and in the play: She has to keep Willy within the confines of "normalcy" the best way she can because she knows that he is about to lose his mind, if he has not already done so. Therefore, it is safe to say that, in trying to keep a strong front in the household, by keeping the head of the household afloat, Linda has relinquished all expectations of her as a mother in favor of being a wife. 

Notice the description that Miller makes of Linda in the play's directions:

Death of a Salesman

....she has developed an iron repression of her exceptions to Willy’s behavior — she more than loves him, she admires him, as though his mercurial nature, his temper, his massive dreams and little cruelties, served her only as sharp reminders of the turbulent longings within him, longings which she shares but lacks the temperament to utter and follow to their end.

When it comes down to it, Linda Loman is her husband's number-one champion. She supports him in everything he does, even though she is more than aware he is not perfect. In fact, she seems quite aware that Willy is suffering from delusions of grandeur.

Even though Willy sometimes treats her dismissively (such as when he yells at her to shut up when she tries chiming into a conversation with her own advice) and the play hints that she might know about Willy's past extramarital affairs, Linda continues to dote on and support him. She even appears to bear him no ill will, knowing that despite the fact that he is not a "great man," he still deserves to live and die with dignity, not like "an old dog."

In many ways, Linda's life is as tragic as Willy's. She represses her own needs in order to keep Willy happy. Unlike Willy, she is levelheaded and realistic, which makes it all the more unwise when she goes along with his unhealthy fantasies or tries to shield him from the pain that would come from waking up from them. She keeps herself subservient and tries to have the men work things out, but in the end, Willy kills himself, leaving Linda quite—alone even if the house she and Willy shared is now paid for in full.

When Willy returns home, Linda rushes to meet him. He is clearly exhausted, and her actions convey both concern and support. Willy evades her questions when she asks what has happened, but Linda refuses to be brushed aside easily.

Instead, her comments indicate that Linda is willing to make excuses for Willy's troubles. When he comments that the car "kept going off on to the shoulder," he ends the statement with "y'know?" Willie wants Linda to agree with the statement even though she wasn't there, and she quickly complies. Linda maintains that it was probably the "steering" which was causing the issues. When Willie then adds that he drove for five minutes without being able to recall a thing about that period of time, Linda assures him that it was probably an issue with his glasses. Linda is clearly grasping here; an inability to see because of difficulties with eyesight could not have been the source of Willie's mental distraction. Still, Linda desperately offers up any support she can generate. When Willie explains that he could "see everything" just fine, she comments with resignation that he really needs to "take a rest."

This early characterization demonstrates that Linda isn't willing to ask Willie difficult questions or to contradict his claims. Instead, she approaches Willie with a gentle temperament and tries to bolster his feelings of self-confidence.

Linda is probably one of the most insightful characters in the drama.  Linda is one who fully understands the frailty of her husband.  She understands how tough it is for him, given the world in which he is competing as well as his own sensibility.  Linda is not a practitioner of "tough love" or one who brings the harshness of the world into her love and reverence for her husband.  She is not a doormat.  Rather, she possesses a quiet strength and reservoir for patience that makes her such a powerful figure.  Miller's inclusion of Linda's characterization reminds the audience how off Willy is in his assessment of what defines success.  Any human being who has a partner like Linda has already embodied success.  Linda is devoted to Willy, offering to essentially operate as his shelter from the storm.  When Linda is referred to as "more than she actually is," it is a stark contrast of how loyal and devoted she is to her husband and ensuring that her love for and of him is one that provides a potential avenue for redemption.  Even if he fails to recognize it, Miller's characterization of Linda's loving treatment of Willy demands that the audience understand that Willy really was "something" for having a partner in his life like Linda.